Max-Bisections of H -free graphs
A bisection of a graph G is a partition of its vertex set into two sets which differ in size by at most 1, and its size is the number of edges between the two sets. The Max-Bisection problem is to find a bisection of G maximizing its size. An ( l , r ) -fan is a graph on ( r − 1 ) l + 1 vertices con...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Hou, Jianfeng [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2020transfer abstract |
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| Übergeordnetes Werk: |
Enthalten in: A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations - Guo, Bangwei ELSEVIER, 2023, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:343 ; year:2020 ; number:1 ; pages:0 |
| Links: |
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| DOI / URN: |
10.1016/j.disc.2019.07.006 |
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| 520 | |a A bisection of a graph G is a partition of its vertex set into two sets which differ in size by at most 1, and its size is the number of edges between the two sets. The Max-Bisection problem is to find a bisection of G maximizing its size. An ( l , r ) -fan is a graph on ( r − 1 ) l + 1 vertices consisting of l cliques of order r that intersect in exactly one common vertex. Let G be a connected graph with n vertices, m edges, and minimum degree at least 2. In this paper, we show that if G contains neither K 2 , l nor ( l , 4 ) -fan, then G has a bisection of size at least m ∕ 2 + ( n − l + 1 ) ∕ 4 , which improves the result given by Jin and Xu. As a corollary, it implies that every connected graph with n vertices, m edges, and minimum degree at least 2 and without cycles of length 4 has a bisection of size at least m ∕ 2 + ( n − 1 ) ∕ 4 . This improves a result given by Fan, Hou and Yu. | ||
| 520 | |a A bisection of a graph G is a partition of its vertex set into two sets which differ in size by at most 1, and its size is the number of edges between the two sets. The Max-Bisection problem is to find a bisection of G maximizing its size. An ( l , r ) -fan is a graph on ( r − 1 ) l + 1 vertices consisting of l cliques of order r that intersect in exactly one common vertex. Let G be a connected graph with n vertices, m edges, and minimum degree at least 2. In this paper, we show that if G contains neither K 2 , l nor ( l , 4 ) -fan, then G has a bisection of size at least m ∕ 2 + ( n − l + 1 ) ∕ 4 , which improves the result given by Jin and Xu. As a corollary, it implies that every connected graph with n vertices, m edges, and minimum degree at least 2 and without cycles of length 4 has a bisection of size at least m ∕ 2 + ( n − 1 ) ∕ 4 . This improves a result given by Fan, Hou and Yu. | ||
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10.1016/j.disc.2019.07.006 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000000831.pica (DE-627)ELV048695351 (ELSEVIER)S0012-365X(19)30244-4 DE-627 ger DE-627 rakwb eng 610 VZ 44.64 bkl 44.32 bkl Hou, Jianfeng verfasserin aut Max-Bisections of H -free graphs 2020transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier A bisection of a graph G is a partition of its vertex set into two sets which differ in size by at most 1, and its size is the number of edges between the two sets. The Max-Bisection problem is to find a bisection of G maximizing its size. An ( l , r ) -fan is a graph on ( r − 1 ) l + 1 vertices consisting of l cliques of order r that intersect in exactly one common vertex. Let G be a connected graph with n vertices, m edges, and minimum degree at least 2. In this paper, we show that if G contains neither K 2 , l nor ( l , 4 ) -fan, then G has a bisection of size at least m ∕ 2 + ( n − l + 1 ) ∕ 4 , which improves the result given by Jin and Xu. As a corollary, it implies that every connected graph with n vertices, m edges, and minimum degree at least 2 and without cycles of length 4 has a bisection of size at least m ∕ 2 + ( n − 1 ) ∕ 4 . This improves a result given by Fan, Hou and Yu. A bisection of a graph G is a partition of its vertex set into two sets which differ in size by at most 1, and its size is the number of edges between the two sets. The Max-Bisection problem is to find a bisection of G maximizing its size. An ( l , r ) -fan is a graph on ( r − 1 ) l + 1 vertices consisting of l cliques of order r that intersect in exactly one common vertex. Let G be a connected graph with n vertices, m edges, and minimum degree at least 2. In this paper, we show that if G contains neither K 2 , l nor ( l , 4 ) -fan, then G has a bisection of size at least m ∕ 2 + ( n − l + 1 ) ∕ 4 , which improves the result given by Jin and Xu. As a corollary, it implies that every connected graph with n vertices, m edges, and minimum degree at least 2 and without cycles of length 4 has a bisection of size at least m ∕ 2 + ( n − 1 ) ∕ 4 . This improves a result given by Fan, Hou and Yu. Max-Bisection Elsevier ( l , 4 ) -fan Elsevier Cycle Elsevier Yan, Juan oth Enthalten in Elsevier Guo, Bangwei ELSEVIER A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations 2023 Amsterdam [u.a.] (DE-627)ELV009312048 volume:343 year:2020 number:1 pages:0 https://doi.org/10.1016/j.disc.2019.07.006 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 44.64 Radiologie VZ 44.32 Medizinische Mathematik medizinische Statistik VZ AR 343 2020 1 0 |
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10.1016/j.disc.2019.07.006 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000000831.pica (DE-627)ELV048695351 (ELSEVIER)S0012-365X(19)30244-4 DE-627 ger DE-627 rakwb eng 610 VZ 44.64 bkl 44.32 bkl Hou, Jianfeng verfasserin aut Max-Bisections of H -free graphs 2020transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier A bisection of a graph G is a partition of its vertex set into two sets which differ in size by at most 1, and its size is the number of edges between the two sets. The Max-Bisection problem is to find a bisection of G maximizing its size. An ( l , r ) -fan is a graph on ( r − 1 ) l + 1 vertices consisting of l cliques of order r that intersect in exactly one common vertex. Let G be a connected graph with n vertices, m edges, and minimum degree at least 2. In this paper, we show that if G contains neither K 2 , l nor ( l , 4 ) -fan, then G has a bisection of size at least m ∕ 2 + ( n − l + 1 ) ∕ 4 , which improves the result given by Jin and Xu. As a corollary, it implies that every connected graph with n vertices, m edges, and minimum degree at least 2 and without cycles of length 4 has a bisection of size at least m ∕ 2 + ( n − 1 ) ∕ 4 . This improves a result given by Fan, Hou and Yu. A bisection of a graph G is a partition of its vertex set into two sets which differ in size by at most 1, and its size is the number of edges between the two sets. The Max-Bisection problem is to find a bisection of G maximizing its size. An ( l , r ) -fan is a graph on ( r − 1 ) l + 1 vertices consisting of l cliques of order r that intersect in exactly one common vertex. Let G be a connected graph with n vertices, m edges, and minimum degree at least 2. In this paper, we show that if G contains neither K 2 , l nor ( l , 4 ) -fan, then G has a bisection of size at least m ∕ 2 + ( n − l + 1 ) ∕ 4 , which improves the result given by Jin and Xu. As a corollary, it implies that every connected graph with n vertices, m edges, and minimum degree at least 2 and without cycles of length 4 has a bisection of size at least m ∕ 2 + ( n − 1 ) ∕ 4 . This improves a result given by Fan, Hou and Yu. Max-Bisection Elsevier ( l , 4 ) -fan Elsevier Cycle Elsevier Yan, Juan oth Enthalten in Elsevier Guo, Bangwei ELSEVIER A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations 2023 Amsterdam [u.a.] (DE-627)ELV009312048 volume:343 year:2020 number:1 pages:0 https://doi.org/10.1016/j.disc.2019.07.006 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 44.64 Radiologie VZ 44.32 Medizinische Mathematik medizinische Statistik VZ AR 343 2020 1 0 |
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10.1016/j.disc.2019.07.006 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000000831.pica (DE-627)ELV048695351 (ELSEVIER)S0012-365X(19)30244-4 DE-627 ger DE-627 rakwb eng 610 VZ 44.64 bkl 44.32 bkl Hou, Jianfeng verfasserin aut Max-Bisections of H -free graphs 2020transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier A bisection of a graph G is a partition of its vertex set into two sets which differ in size by at most 1, and its size is the number of edges between the two sets. The Max-Bisection problem is to find a bisection of G maximizing its size. An ( l , r ) -fan is a graph on ( r − 1 ) l + 1 vertices consisting of l cliques of order r that intersect in exactly one common vertex. Let G be a connected graph with n vertices, m edges, and minimum degree at least 2. In this paper, we show that if G contains neither K 2 , l nor ( l , 4 ) -fan, then G has a bisection of size at least m ∕ 2 + ( n − l + 1 ) ∕ 4 , which improves the result given by Jin and Xu. As a corollary, it implies that every connected graph with n vertices, m edges, and minimum degree at least 2 and without cycles of length 4 has a bisection of size at least m ∕ 2 + ( n − 1 ) ∕ 4 . This improves a result given by Fan, Hou and Yu. A bisection of a graph G is a partition of its vertex set into two sets which differ in size by at most 1, and its size is the number of edges between the two sets. The Max-Bisection problem is to find a bisection of G maximizing its size. An ( l , r ) -fan is a graph on ( r − 1 ) l + 1 vertices consisting of l cliques of order r that intersect in exactly one common vertex. Let G be a connected graph with n vertices, m edges, and minimum degree at least 2. In this paper, we show that if G contains neither K 2 , l nor ( l , 4 ) -fan, then G has a bisection of size at least m ∕ 2 + ( n − l + 1 ) ∕ 4 , which improves the result given by Jin and Xu. As a corollary, it implies that every connected graph with n vertices, m edges, and minimum degree at least 2 and without cycles of length 4 has a bisection of size at least m ∕ 2 + ( n − 1 ) ∕ 4 . This improves a result given by Fan, Hou and Yu. Max-Bisection Elsevier ( l , 4 ) -fan Elsevier Cycle Elsevier Yan, Juan oth Enthalten in Elsevier Guo, Bangwei ELSEVIER A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations 2023 Amsterdam [u.a.] (DE-627)ELV009312048 volume:343 year:2020 number:1 pages:0 https://doi.org/10.1016/j.disc.2019.07.006 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 44.64 Radiologie VZ 44.32 Medizinische Mathematik medizinische Statistik VZ AR 343 2020 1 0 |
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10.1016/j.disc.2019.07.006 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000000831.pica (DE-627)ELV048695351 (ELSEVIER)S0012-365X(19)30244-4 DE-627 ger DE-627 rakwb eng 610 VZ 44.64 bkl 44.32 bkl Hou, Jianfeng verfasserin aut Max-Bisections of H -free graphs 2020transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier A bisection of a graph G is a partition of its vertex set into two sets which differ in size by at most 1, and its size is the number of edges between the two sets. The Max-Bisection problem is to find a bisection of G maximizing its size. An ( l , r ) -fan is a graph on ( r − 1 ) l + 1 vertices consisting of l cliques of order r that intersect in exactly one common vertex. Let G be a connected graph with n vertices, m edges, and minimum degree at least 2. In this paper, we show that if G contains neither K 2 , l nor ( l , 4 ) -fan, then G has a bisection of size at least m ∕ 2 + ( n − l + 1 ) ∕ 4 , which improves the result given by Jin and Xu. As a corollary, it implies that every connected graph with n vertices, m edges, and minimum degree at least 2 and without cycles of length 4 has a bisection of size at least m ∕ 2 + ( n − 1 ) ∕ 4 . This improves a result given by Fan, Hou and Yu. A bisection of a graph G is a partition of its vertex set into two sets which differ in size by at most 1, and its size is the number of edges between the two sets. The Max-Bisection problem is to find a bisection of G maximizing its size. An ( l , r ) -fan is a graph on ( r − 1 ) l + 1 vertices consisting of l cliques of order r that intersect in exactly one common vertex. Let G be a connected graph with n vertices, m edges, and minimum degree at least 2. In this paper, we show that if G contains neither K 2 , l nor ( l , 4 ) -fan, then G has a bisection of size at least m ∕ 2 + ( n − l + 1 ) ∕ 4 , which improves the result given by Jin and Xu. As a corollary, it implies that every connected graph with n vertices, m edges, and minimum degree at least 2 and without cycles of length 4 has a bisection of size at least m ∕ 2 + ( n − 1 ) ∕ 4 . This improves a result given by Fan, Hou and Yu. Max-Bisection Elsevier ( l , 4 ) -fan Elsevier Cycle Elsevier Yan, Juan oth Enthalten in Elsevier Guo, Bangwei ELSEVIER A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations 2023 Amsterdam [u.a.] (DE-627)ELV009312048 volume:343 year:2020 number:1 pages:0 https://doi.org/10.1016/j.disc.2019.07.006 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 44.64 Radiologie VZ 44.32 Medizinische Mathematik medizinische Statistik VZ AR 343 2020 1 0 |
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10.1016/j.disc.2019.07.006 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000000831.pica (DE-627)ELV048695351 (ELSEVIER)S0012-365X(19)30244-4 DE-627 ger DE-627 rakwb eng 610 VZ 44.64 bkl 44.32 bkl Hou, Jianfeng verfasserin aut Max-Bisections of H -free graphs 2020transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier A bisection of a graph G is a partition of its vertex set into two sets which differ in size by at most 1, and its size is the number of edges between the two sets. The Max-Bisection problem is to find a bisection of G maximizing its size. An ( l , r ) -fan is a graph on ( r − 1 ) l + 1 vertices consisting of l cliques of order r that intersect in exactly one common vertex. Let G be a connected graph with n vertices, m edges, and minimum degree at least 2. In this paper, we show that if G contains neither K 2 , l nor ( l , 4 ) -fan, then G has a bisection of size at least m ∕ 2 + ( n − l + 1 ) ∕ 4 , which improves the result given by Jin and Xu. As a corollary, it implies that every connected graph with n vertices, m edges, and minimum degree at least 2 and without cycles of length 4 has a bisection of size at least m ∕ 2 + ( n − 1 ) ∕ 4 . This improves a result given by Fan, Hou and Yu. A bisection of a graph G is a partition of its vertex set into two sets which differ in size by at most 1, and its size is the number of edges between the two sets. The Max-Bisection problem is to find a bisection of G maximizing its size. An ( l , r ) -fan is a graph on ( r − 1 ) l + 1 vertices consisting of l cliques of order r that intersect in exactly one common vertex. Let G be a connected graph with n vertices, m edges, and minimum degree at least 2. In this paper, we show that if G contains neither K 2 , l nor ( l , 4 ) -fan, then G has a bisection of size at least m ∕ 2 + ( n − l + 1 ) ∕ 4 , which improves the result given by Jin and Xu. As a corollary, it implies that every connected graph with n vertices, m edges, and minimum degree at least 2 and without cycles of length 4 has a bisection of size at least m ∕ 2 + ( n − 1 ) ∕ 4 . This improves a result given by Fan, Hou and Yu. Max-Bisection Elsevier ( l , 4 ) -fan Elsevier Cycle Elsevier Yan, Juan oth Enthalten in Elsevier Guo, Bangwei ELSEVIER A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations 2023 Amsterdam [u.a.] (DE-627)ELV009312048 volume:343 year:2020 number:1 pages:0 https://doi.org/10.1016/j.disc.2019.07.006 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 44.64 Radiologie VZ 44.32 Medizinische Mathematik medizinische Statistik VZ AR 343 2020 1 0 |
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A bisection of a graph G is a partition of its vertex set into two sets which differ in size by at most 1, and its size is the number of edges between the two sets. The Max-Bisection problem is to find a bisection of G maximizing its size. An ( l , r ) -fan is a graph on ( r − 1 ) l + 1 vertices consisting of l cliques of order r that intersect in exactly one common vertex. Let G be a connected graph with n vertices, m edges, and minimum degree at least 2. In this paper, we show that if G contains neither K 2 , l nor ( l , 4 ) -fan, then G has a bisection of size at least m ∕ 2 + ( n − l + 1 ) ∕ 4 , which improves the result given by Jin and Xu. As a corollary, it implies that every connected graph with n vertices, m edges, and minimum degree at least 2 and without cycles of length 4 has a bisection of size at least m ∕ 2 + ( n − 1 ) ∕ 4 . This improves a result given by Fan, Hou and Yu. |
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A bisection of a graph G is a partition of its vertex set into two sets which differ in size by at most 1, and its size is the number of edges between the two sets. The Max-Bisection problem is to find a bisection of G maximizing its size. An ( l , r ) -fan is a graph on ( r − 1 ) l + 1 vertices consisting of l cliques of order r that intersect in exactly one common vertex. Let G be a connected graph with n vertices, m edges, and minimum degree at least 2. In this paper, we show that if G contains neither K 2 , l nor ( l , 4 ) -fan, then G has a bisection of size at least m ∕ 2 + ( n − l + 1 ) ∕ 4 , which improves the result given by Jin and Xu. As a corollary, it implies that every connected graph with n vertices, m edges, and minimum degree at least 2 and without cycles of length 4 has a bisection of size at least m ∕ 2 + ( n − 1 ) ∕ 4 . This improves a result given by Fan, Hou and Yu. |
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A bisection of a graph G is a partition of its vertex set into two sets which differ in size by at most 1, and its size is the number of edges between the two sets. The Max-Bisection problem is to find a bisection of G maximizing its size. An ( l , r ) -fan is a graph on ( r − 1 ) l + 1 vertices consisting of l cliques of order r that intersect in exactly one common vertex. Let G be a connected graph with n vertices, m edges, and minimum degree at least 2. In this paper, we show that if G contains neither K 2 , l nor ( l , 4 ) -fan, then G has a bisection of size at least m ∕ 2 + ( n − l + 1 ) ∕ 4 , which improves the result given by Jin and Xu. As a corollary, it implies that every connected graph with n vertices, m edges, and minimum degree at least 2 and without cycles of length 4 has a bisection of size at least m ∕ 2 + ( n − 1 ) ∕ 4 . This improves a result given by Fan, Hou and Yu. |
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