Results 201 to 210 of about 153,964 (249)

The generalized connectivity of the line graph and the total graph for the complete bipartite graph

Applied Mathematics and Computation, 2019
The generalized k-connectivity κk(G) of a graph G, introduced by Hager (1985), is a natural generalization of the concept of connectivity κ(G), which is just for k = 2 . This parameter is often used to measure the capability of a network G to connect any
Yinkui Li, Ruijuan Gu, H. Lei
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Complete (2,2) Bipartite Graphs

Malaysian Journal of Mathematical Sciences, 2022
A 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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Paintability of Complete Bipartite Graphs

Discrete Applied Mathematics, 2023
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A complete bipartite graph without properly colored cycles of length four

Journal of Graph Theory, 2019
A subgraph of an edge‐colored graph is said to be properly colored, or shortly PC, if any two adjacent edges have different colors. Fujita, Li, and Zhang gave a decomposition theorem for edge‐colorings of complete bipartite graphs without PC C4 . However,
Roman Cada, K. Ozeki, Kiyoshi Yoshimoto
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Packings by Complete Bipartite Graphs

SIAM Journal on Algebraic Discrete Methods, 1986
Summary: Given any set \({\mathcal B}\) of complete bipartite graphs, we ask whether a graph H admits a \({\mathcal B}\)-factor, i.e., a spanning subgraph, each of whose components is a member of \({\mathcal B}\). More generally, we seek in H a maximum \({\mathcal B}\)-packing, i.e., a \({\mathcal B}\)-factor of a maximum size subgraph of H.
Hell, P., Kirkpatrick, D. G.
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Decomposition of the complete bipartite graph with a 1-factor removed into paths and stars

Contributions Discret. Math., 2018
Let P_k denote a path on k vertices, and let S_k denote a star with k edges. For graphs F, G, and H, a decomposition of F is a set of edge-disjoint subgraphs of F whose union is F. A (G,H)-decomposition of F is a decomposition of F into copies of G and H
Jenq-Jong Lin, Hung-Chih Lee
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On bisections of graphs without complete bipartite graphs

Journal of Graph Theory, 2021
A bisection of a graph is a bipartition of its vertex set in which the two classes differ in size by at most one. For a random bisection of a graph with m edges, one expects m ∕ 4 edges spans in one vertex class.
Jianfeng Hou, Shufei Wu
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Parallelogram polyominoes, the sandpile model on a complete bipartite graph, and a q, t-Narayana polynomial

Journal of Combinatorial Theory, 2012
We classify recurrent configurations of the sandpile model on the complete bipartite graph K"m","n in which one designated vertex is a sink. We present a bijection from these recurrent configurations to decorated parallelogram polyominoes whose bounding ...
M. Dukes, Y. L. Borgne
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Packing two bipartite graphs into a complete bipartite graph

Journal of Graph Theory, 1997
A 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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