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Graph Ear Decompositions and Graph Embeddings
SIAM Journal on Discrete Mathematics, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, Jianer, Kanchi, Saroja P.
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I/O Efficient Core Graph Decomposition: Application to Degeneracy Ordering
IEEE Transactions on Knowledge and Data Engineering, 2019Core decomposition is a fundamental graph problem with a large number of applications. Most existing approaches for core decomposition assume that the graph is kept in memory of a machine.
Dong Wen +4 more
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Induced Decompositions of Graphs
Journal of Graph Theory, 2012AbstractWe 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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Joint Graph Decomposition & Node Labeling: Problem, Algorithms, Applications
Computer Vision and Pattern Recognition, 2016We state a combinatorial optimization problem whose feasible solutions define both a decomposition and a node labeling of a given graph. This problem offers a common mathematical abstraction of seemingly unrelated computer vision tasks, including ...
Evgeny Levinkov +9 more
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P4-decompositions of regular graphs
Journal of Graph Theory, 1999It 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 +2 more
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Petersen Graph Decompositions of Complete Multipartite Graphs
Graphs and Combinatorics, 2010zbMATH 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, 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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S5-DECOMPOSITION OF KNESER GRAPHS
South East Asian J. of Mathematics and Mathematical Sciences, 2022Let 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, 1982A 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
2021The 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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