Results 221 to 230 of about 46,387 (243)

Graph Decomposition of Slim Graphs

Graphs and Combinatorics, 1999
Let \(H\) be a fixed graph. An \(H\)-decomposition of an input graph \(G\) is a partition of the edge set of \(G\) such that each part forms a subgraph isomorphic to \(H\). This problem is known to be NP-complete as soon as \(H\) has a component with at least three edges. (This was conjectured by Holyer, and proved independently by \textit{D. Dor} and \
Caro, Yair, Yuster, Raphael
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Graph Ear Decompositions and Graph Embeddings

SIAM Journal on Discrete Mathematics, 1999
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Chen, Jianer, Kanchi, Saroja P.
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Induced Decompositions of Graphs

Journal of Graph Theory, 2012
AbstractWe consider those graphs G that admit decompositions into copies of a fixed graph F, each copy being an induced subgraph of G. We are interested in finding the extremal graphs with this property, that is, those graphs G on n vertices with the maximum possible number of edges. We discuss the cases where F is a complete equipartite graph, a cycle,
Bondy, J. Adrian, Szwarcfiter, Jayme L.
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P4-decompositions of regular graphs

Journal of Graph Theory, 1999
It is shown that every simple \(r\)-regular graph \(G\) admits a balanced \(P_4\)-decomposition if \(r \equiv 0\pmod 3\) and \(G\) has no cut-edge when \(r\) is odd. It is also shown that a connected 4-regular graph \(G\) admits a \(P_4\)-decomposition if and only if \(| E(G)| \equiv 0\pmod 3\) by characterizing graphs of maximum degree 4 that admit a ...
Heinrich, Katherine, Liu, Jiping, Yu, Minli   +2 more
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Petersen Graph Decompositions of Complete Multipartite Graphs

Graphs and Combinatorics, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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