Results 281 to 290 of about 1,017,247 (314)
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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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Bipartite graphs as polynomials and polynomials as bipartite graphs
Journal of Algebra and its Applications, 2019The aim of this paper is to show that any finite undirected bipartite graph can be considered as a polynomial [Formula: see text], and any directed finite bipartite graph can be considered as a polynomial [Formula: see text], and vise verse. We also show
A. Grinblat, V. Lopatkin
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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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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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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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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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On the contour of bipartite graphs
Discrete Applied Mathematics, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Danilo Artigas, R. Sritharan
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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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