Results 261 to 270 of about 3,489,698 (302)
On the vulnerability of permutation graphs of complete and complete bipartite graphs
, 1991 The integrity of a graph \(G\) is defined as \(\min\{| S|+m(G-S)\}\) taken over all subsets \(S\) of \(V(G)\), where \(m(G-S)\) is the order of the largest component of \(G-S\). The toughness of \(G\) is defined as \(\min\{| S|/w(G-S)\}\) taken over all disconnecting subsets \(S\) of \(G\), where \(w(G-S)\) is the number of components of \(G-S\).
Guichard, D. +2 more
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Completely Disconnecting the Complete Graph
SIAM Journal on Discrete Mathematics, 2000In this paper we consider procedures for completely disconnecting a complete graph on n vertices $K_n$. By this we simply mean that we wish to remove all of the edges of $K_n$ in a sequence of steps by which the graph $K_n$ is successively transformed into the empty graph on n vertices.
John Ginsburg, Bill Sands
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On a Decomposition of Complete Graphs
Graphs and Combinatorics, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hadi Kharaghani, Rouzbeh Torabi
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On the Decomposition of Graphs into Complete Bipartite Graphs
Graphs and Combinatorics, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jinquan Dong, Yanpei Liu
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Critical Groups for Complete Multipartite Graphs and Cartesian Products of Complete Graphs
Journal of Graph Theory, 2003 . The critical group of a connected graph is a finite abelian group, whose order is the number of spanning trees in the graph, and which is closely related to the graph Laplacian.
Victor Schorr Reiner
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Detachments of Complete Graphs
Combinatorics, Probability and Computing, 2005A detachment of a graph $G$ is formed by splitting each vertex into one or more subvertices, and sharing the incident edges arbitrarily among the subvertices. In this paper we consider the question of whether a graph $H$ is a detachment of some complete graph $K_n$.
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The complete closure of a graph
Journal of Graph Theory, 1993AbstractWe define the complete closure number cc(G) of a graph G of order n as the greatest integer k ≤ 2n − 3 such that the kth Bondy‐Chvátal closure Clk(G) is complete, and give some necessary or sufficient conditions for a graph to have cc(G) = k.
Ralph J. Faudree +3 more
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2013
Let T 1, T 2,…, T k be spanning trees in a graph G. If for any two vertices x, y of G, the paths from x to y in T 1, T 2,…, T k are vertex-disjoint except end vertices x and y, then T 1, T 2,…, T k are called completely independent spanning trees in G. In 2001, Hasunuma gave a conjecture that there are k completely independent spanning trees in any 2k ...
Kung-Jui Pai +3 more
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Let T 1, T 2,…, T k be spanning trees in a graph G. If for any two vertices x, y of G, the paths from x to y in T 1, T 2,…, T k are vertex-disjoint except end vertices x and y, then T 1, T 2,…, T k are called completely independent spanning trees in G. In 2001, Hasunuma gave a conjecture that there are k completely independent spanning trees in any 2k ...
Kung-Jui Pai +3 more
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The Coarseness of the Complete Graph
Canadian Journal of Mathematics, 1968The coarseness, c(G), of a graph G is the maximum number of edge-disjoint, non-planar subgraphs of G. We consider only the complete graph, Kp, on p vertices here. For p = 3r, Erdös conjectured that the coarseness was , but it has been shown (1) that1where square brackets denote integer part.
Guy, R. K., Beineke, L. W.
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