Results 241 to 250 of about 617,805 (269)
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Combinatorica, 1992
Two simple graphs \(G\) and \(H\) can be packed if \(G\) is isomorphic to a subgraph of the complement \(\overline H\) of \(H\). A sufficient condition is known for the existence of packing in terms of the product of the maximal degrees of \(G\) and \(H\).
Péter Hajnal, Mario Szegedy
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Two simple graphs \(G\) and \(H\) can be packed if \(G\) is isomorphic to a subgraph of the complement \(\overline H\) of \(H\). A sufficient condition is known for the existence of packing in terms of the product of the maximal degrees of \(G\) and \(H\).
Péter Hajnal, Mario Szegedy
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Graphs and Combinatorics, 1994
For many years a characterization of those graphs \(G\) so that \(G\cong L(H)\), where \(L(H)\) is the line graph of the graph \(H\), has been known. The authors generalize this notion as follows. A graphoidal cover \(\psi_ G\) of \(G\) is a partition of \(E(G)\) into paths so that each vertex is the interior vertex of at most one path.
S. Arumugam 0001, C. Pakkiam
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For many years a characterization of those graphs \(G\) so that \(G\cong L(H)\), where \(L(H)\) is the line graph of the graph \(H\), has been known. The authors generalize this notion as follows. A graphoidal cover \(\psi_ G\) of \(G\) is a partition of \(E(G)\) into paths so that each vertex is the interior vertex of at most one path.
S. Arumugam 0001, C. Pakkiam
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Embeddings of bipartite graphs
Journal of Graph Theory, 1983AbstractIf G is a bipartite graph with bipartition A, B then let Gm,n(A, B) be obtained from G by replacing each vertex a of A by an independent set a1, …, am, each vertex b of B by an independent set b1,…, bn, and each edge ab of G by the complete bipartite graph with edges aibj (1 ≤ i ≤ m and 1 ≤ j ≤ n).
Mohammed Abu-Sbeih, Torrence D. Parsons
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Packing two bipartite graphs into a complete bipartite graph
Journal of Graph Theory, 1997A bipartite graph \(G\) admits an \((a,b)\)-bipartition if \(G\) has a bipartition \((X,Y)\) such that \(|X|=a\) and \(|Y|=b\). Two bipartite graphs \(G\) and \(H\) are compatible if, for some integers \(a\) and \(b\), both \(G\) and \(H\) admit an \((a,b)\)-bipartition. In the paper it is proved that any two compatible \(C_4\)-free bipartite graphs of
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On judicious bipartitions of graphs
Combinatorica, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jie Ma 0002, Xingxing Yu
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Bipartitions of oriented graphs
Journal of Combinatorial Theory, Series B, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jianfeng Hou, Shufei Wu
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ACM Transactions on Algorithms, 2006
Graph H is a root of graph G if there exists a positive integer k such that x and y are adjacent in G if and only if their distance in H is at most k
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Graph H is a root of graph G if there exists a positive integer k such that x and y are adjacent in G if and only if their distance in H is at most k
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Bichromaticity of bipartite graphs
Journal of Graph Theory, 1985AbstractLet B be a bipartite graph with edge set E and vertex bipartition M, N. The bichromaticity β(B) is defined as the maximum number β such that a complete bipartite graph on β vertices is obtainable from B by a sequence of identifications of vertices of M or vertices of N. Let μ = max{∣M∣, ∣N∣}. Harary, Hsu, and Miller proved that β(B) ≥ μ + 1 and
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SIAM Journal on Discrete Mathematics, 2009
For each $s\geq2$, there exists $m_0$ such that the following holds for all $m\geq m_0$: Let $G$ be a bipartite graph with $n=ms$ vertices in each partition set. If $m$ is odd and minimum degree $\delta(G)\geq\frac{n+3s}{2}-2$, then $G$ contains $m$ vertex-disjoint copies of $K_{s,s}$. If $m$ is even, the same holds under the weaker condition $\delta(G)
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For each $s\geq2$, there exists $m_0$ such that the following holds for all $m\geq m_0$: Let $G$ be a bipartite graph with $n=ms$ vertices in each partition set. If $m$ is odd and minimum degree $\delta(G)\geq\frac{n+3s}{2}-2$, then $G$ contains $m$ vertex-disjoint copies of $K_{s,s}$. If $m$ is even, the same holds under the weaker condition $\delta(G)
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Bipartite Graphs and Coverings
2011In many real world applications, data are organized by coverings, instead of partitions. Covering-based rough sets have been proposed to cope with this type of data. Covering-based rough set theory is more general than rough set theory, then there is a need to employ sophisticated theories to make it more adaptive to applications.
Shiping Wang +2 more
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