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Canonical Decomposition of Graphs
1996Summary: 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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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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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
2009In 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, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chartrand, Gary +3 more
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Decomposition of Graphs into Chains
Bulletin of the London Mathematical Society, 1986A 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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Graph Searching and Graph Decompositions
2010Graph searching is a game where a team of mobile agents must catch a fugitive hidden in a network (modelled by a graph). Equivalently, graph searching may be deļ¬ned in terms of clearing a contaminated network. Besides of its practical interests, graph searching has been widely studied for its relationship with important graph parameters, in particular ...
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