Results 171 to 180 of about 6,109 (206)
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Complete (2,2) Bipartite Graphs
Malaysian Journal of Mathematical Sciences, 2022A bipartite graph G can be treated as a (1,1) bipartite graph in the sense that, no two vertices in the same part are at distance one from each other. A (2,2) bipartite graph is an extension of the above concept in which no two vertices in the same part are at distance two from each other.
Hanif, S., Bhat, K. A., Sudhakara, G.
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Physical Review Letters, 1987
Replica-symmetric solutions of the graph-bipartitioning problem with finite connectivity are presented. With the constraint ${sum}_{\mathrm{i}=1}^{\mathrm{N}}$${\mathrm{S}}_{\mathrm{i}}$=0 strictly enforced, another solution can be obtained, which gives a lower cost function than that given by the spin-glass solution.
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Replica-symmetric solutions of the graph-bipartitioning problem with finite connectivity are presented. With the constraint ${sum}_{\mathrm{i}=1}^{\mathrm{N}}$${\mathrm{S}}_{\mathrm{i}}$=0 strictly enforced, another solution can be obtained, which gives a lower cost function than that given by the spin-glass solution.
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Combinatorics, Probability and Computing, 1997
In this note we give a probabilistic proof of the existence of an n-vertex graph Gn, n=1, 2, [ctdot ], such that, for some constant c>0, the edges of Gn cannot be covered by n−c log n complete bipartite subgraphs of Gn. This result improves a previous bound due to F. R. K. Chung and is the best possible up to a constant.
Rödl, Vojtěch, Ruciński, Andrzej
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In this note we give a probabilistic proof of the existence of an n-vertex graph Gn, n=1, 2, [ctdot ], such that, for some constant c>0, the edges of Gn cannot be covered by n−c log n complete bipartite subgraphs of Gn. This result improves a previous bound due to F. R. K. Chung and is the best possible up to a constant.
Rödl, Vojtěch, Ruciński, Andrzej
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Maximal Energy Bipartite Graphs
Graphs and Combinatorics, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Koolen, Jack H., Moulton, Vincent
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Canadian Journal of Mathematics, 1958
For the purpose of analysing bipartite graphs (hereinafter called simply graphs) the concept of an exterior covering is introduced. In terms of this concept it is possible in a natural way to decompose any graph into two parts, an inadmissible part and a core.
Dulmage, A. L., Mendelsohn, N. S.
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For the purpose of analysing bipartite graphs (hereinafter called simply graphs) the concept of an exterior covering is introduced. In terms of this concept it is possible in a natural way to decompose any graph into two parts, an inadmissible part and a core.
Dulmage, A. L., Mendelsohn, N. S.
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Bipartite graphs as polynomials and polynomials as bipartite graphs
Journal of Algebra and Its Applications, 2020The 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 that the multiplication in the semirings [Formula: see text], [Formula: see text] corresponds to an
Grinblat, Andrey, Lopatkin, Viktor
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BIPARTITE PERMUTATION GRAPHS ARE RECONSTRUCTIBLE
Discrete Mathematics, Algorithms and Applications, 2010The graph reconstruction conjecture is a long-standing open problem in graph theory. The conjecture has been verified for all graphs with at most 11 vertices. Further, the conjecture has been verified for regular graphs, trees, disconnected graphs, unit interval graphs, separable graphs with no pendant vertex, outer-planar graphs, and unicyclic graphs.
Kiyomi, Masashi +2 more
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Constructing Unstable Graphs from Bipartite Graphs
Bulletin of the Malaysian Mathematical Sciences SocietyzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Haiyan Jiang, Junyang Zhang
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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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