Results 291 to 300 of about 405,092 (308)

Petersen Graph Decompositions of Complete Multipartite Graphs

Graphs and Combinatorics, 2010
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Wang, Jinhua, Ma, Dengju
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Decompositions of Complete Graphs

Bulletin of the London Mathematical Society, 2000
Summary: 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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S5-DECOMPOSITION OF KNESER GRAPHS

South East Asian J. of Mathematics and Mathematical Sciences, 2022
Let A = {1, 2, 3, ..., n} and Pk(A) denotes the set of all k-element subsets of A. The Kneser graph KGn,2 has the vertex set V (KGn,2)= P2(A) and edge set E(KGn,2) = {XY |X, Y ∈ P2(A) and X ∩ Y = ∅}. A star with k edges is denoted by Sk. In this paper, we show that the graph KGn,2 can be decomposed into S5 if and only if n ≥ 7 and n ≡ 0, 1, 2, 3(mod 5).
Sankari, C., Sangeetha, R., Arthi, K.
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Decomposition of Directed Graphs

SIAM Journal on Algebraic Discrete Methods, 1982
A composition for directed graphs which generalizes the substitution (or X-join) composition of graphs and digraphs, as well as the graph version of set-family composition, is described. It is proved that a general decomposition theory can be applied to the resulting digraph decomposition.
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Generalizing graph decompositions

2021
The Latin aphorism ‘divide et impera’ conveys a simple, but central idea in mathematics and computer science: ‘split your problem recursively into smaller parts, attack the parts, and conquer the whole’. There is a vast literature on how to do this on graphs.
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Canonical Decomposition of Graphs

1996
Summary: A partition of the vertex set of a graph \(G\) is called canonical if every two elements of the partition induce in \(G\) either a disconnected graph or the complement of a disconnected graph. Thus, every canonical partition of the graph \(G\) can be associated with another graph whose vertices are in a one-to-one correspondence with the ...
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Perfect graph decompositions

Graphs and Combinatorics, 1991
Proved are three theorems presenting upper and lower bounds of the minimum number of perfect subgraphs covering or partitioning either the vertex set or the edge set of a given graph. The weighted versions of both cases are studied, too. All the theorems are based on four lemmas, one of which being proved and published by the author in 1986.
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Graph decompositions and symmetry

2009
In this paper I shall try to review some results which were obtained in the area of factorizations and decompositions of complete graphs admitting an automorphism group with some specified properties. These properties primarily involve the action of the group on the objects of the decomposition, most oftenvertices, but also edges, subgraphs of the ...
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The Decomposition Dimension of Graphs

Graphs and Combinatorics, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chartrand, Gary, Erwin, David, Raines, Michael, Zhang, Ping   +3 more
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Decomposition of Graphs into Chains

Bulletin of the London Mathematical Society, 1986
A one-way infinite chain in a graph is a sequence \(X_0e_0X_1e_1,\ldots\) where \(X_0,X_1,\ldots\) are vertices of \(G\), \(e_0,e_1,\ldots\) are distinct edges of \(G\) and \(e_i\) joins \(X_i\) and \(X_{i+1}\) for \(i=0,1,\ldots\). A two-way infinite chain and a finite chain are defined analogously.
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