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Complete multipartite decompositions of complete graphs and complete n-partite graphs
Applied Mathematics-A Journal of Chinese Universities, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Combinatorica, 2007
Complete partitions of a graph are vertex partitions such that any two classes are related by an arc. The authors compute tight lower and upper bounds for the maximum number of classes in a complete partition. A technique used is that of finding the largest integer \(\beta(G)\) such that there exists a subgraph \(H\subseteq G\) with maximum degree at ...
Magnús M. Halldórsson +3 more
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Complete partitions of a graph are vertex partitions such that any two classes are related by an arc. The authors compute tight lower and upper bounds for the maximum number of classes in a complete partition. A technique used is that of finding the largest integer \(\beta(G)\) such that there exists a subgraph \(H\subseteq G\) with maximum degree at ...
Magnús M. Halldórsson +3 more
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Decompositions of Complete Graphs
Bulletin of the London Mathematical Society, 2000Summary: If \(s_1,s_2,\dots, s_t\) are integers such that \(n-1= s_1+ s_2+\cdots+ s_t\) and such that for each \(i\) \((1\leq i\leq t)\), \(2\leq s_i\leq n-1\) and \(s_in\) is even, then \(K_n\) can be expressed as the union \(G_1\cup G_2\cup\cdots\cup G_t\) of \(t\) edge-disjoint factors, where for each \(i\), \(G_i\) is \(s_i\)-connected.
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Multidecompositions of line graphs of complete graphs
Discrete Mathematics, Algorithms and Applications, 2019By a [Formula: see text]-decomposition of a graph [Formula: see text] we mean a decomposition of [Formula: see text] into [Formula: see text] copies of [Formula: see text] [Formula: see text] copies of [Formula: see text] and [Formula: see text] copies of [Formula: see text], where [Formula: see text] are non-negative integers.
S. Ganesamurthy 0001 +2 more
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Graphs omitting sums of complete graphs
Journal of Graph Theory, 1997There is a finite number of countable graphs omitting \(G\) such that every such graph is embedded into one of them if \(G\) is the vertex disjoint union of complete graphs. This was conjectured by Pach and the reviewer. The required number is determined in some cases.
Gregory L. Cherlin, Niandong Shi
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Contractions to Complete Graphs
1988We survey some extremal problems concerning contraction to complete graphs, including two new theorems of the author. We also show an application to a conjecture of Las Vergnas and Meyniel.
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The genus of the complete multipartite graph and the complete multi-layered graph
ACS/IEEE International Conference on Computer Systems and Applications - AICCSA 2010, 2010The complete multipartite graph and the complete multi-layered graph are both generalizations of the complete bipartite graph. These two kinds of graphs have recursive structure and offer a very flexible choice of network size with respect to a fixed network order. This paper addresses the genus of the complete multipartite graph and the complete multi-
Saïd Bettayeb, Quan T. Nguyen
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THE TOTAL IRREGULARITY STRENGTH OF COMPLETE GRAPHS AND COMPLETE BIPARTITE GRAPHS
Far East Journal of Mathematical Sciences (FJMS), 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tilukay, M. I. +3 more
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Canadian Journal of Mathematics, 1967
In our paper “Magic graphs” (1) we showed that every complete graph Kn with n ⩾ 5 is “magic,” i.e., if the vertex set is indicated {vi} and if eij is the edge joining vi and vj, i ≠ j , then there exists a function α(eij) such that the set {α(eij)} consists of distinct positive rational integers and the vertex sums1have a constant value σ(α) for k = 1,
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In our paper “Magic graphs” (1) we showed that every complete graph Kn with n ⩾ 5 is “magic,” i.e., if the vertex set is indicated {vi} and if eij is the edge joining vi and vj, i ≠ j , then there exists a function α(eij) such that the set {α(eij)} consists of distinct positive rational integers and the vertex sums1have a constant value σ(α) for k = 1,
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Edge disjoint graph spanners of complete graphs and complete digraphs
Proceedings of the Thirtieth Hawaii International Conference on System Sciences, 2002A spanning subgraph S=(V, E') of a connected simple graph (digraph)G=(V, E) is a f(x)-spanner if for any pair of nodes u and v, d/sub S/(u, v)/spl les/f(d/sub G/(u, v)) where d/sub G/ and d/sub S/ are the usual distance functions in graphs (digraphs) G and S, respectively. The delay of the f(x)-spanner is f(x)-x.
Christian Laforest +3 more
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