Results 11 to 20 of about 7,309 (246)
Irredundancy in circular arc graphs
Discrete Applied Mathematics, 1993 An open neighbourhood of a vertex \(x\) in an undirected graph \(G\) is the set \(N(x)\) of all vertices adjacent to \(x\) in \(G\); its closed neighbourhood is \(N[x]=N(x) \cup \{x\}\). For a set \(S\) of vertices set \(N(S)=\bigcup_{x \in S}N(x)\) and \(N[S]=\bigcup_{x \in S} N[x]\). A subset \(X\) of the vertex set of \(G\) is called irredundant (or
Martin Charles Golumbic, Renu C. Laskar
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On coherent configuration of circular-arc graphs [PDF]
Communications in Combinatorics and OptimizationFor any graph, Weisfeiler and Leman assigned the smallest matrix algebra which contains the adjacency matrix of the graph. The coherent configuration underlying this algebra for a graph $\Gamma$ is called the coherent configuration of $\Gamma ...
Fatemeh Raei Barandagh +1 more
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Certifying Algorithms for Recognizing Proper Circular-Arc Graphs and Unit Circular-Arc Graphs
Discrete Applied Mathematics, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Haim Kaplan, Yahav Nussbaum
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On powers of circular arc graphs and proper circular arc graphs
Discrete Applied Mathematics, 1996 Let \(\mathcal K\) denote the class of circular arc graphs. The author gives a new proof that if a graph \(G\in {\mathcal K}\), then the power \(G^n\in {\mathcal K}\) for any positive integer \(n\). Moreover, he proves that if \(G^n\in {\mathcal K}\) then \(G^{n+2}\in {\mathcal K}\) and if \(\text{diam}(G^n)\geq 4\) then \(G^n\in {\mathcal K}\) implies
Flotow, Carsten
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Partial Characterizations of Circular-Arc Graphs
Electronic Notes in Discrete Mathematics, 2008 AbstractA circular‐arc graph is the intersection graph of a family of arcs on a circle. A characterization by forbidden induced subgraphs for this class of graphs is not known, and in this work we present a partial result in this direction. We characterize circular‐arc graphs by a list of minimal forbidden induced subgraphs when the graph belongs to ...
Flavia Bonomo +3 more
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Pathwidth of Circular-Arc Graphs [PDF]
, 2007 The pathwidth of a graph G is the minimum clique number of H minus one, over all interval supergraphs H of G. Although pathwidth is a well-known and well-studied graph parameter, there are extremely few graph classes for which pathwidh is known to be tractable in polynomial time.
Karol Suchan, Ioan Todinca
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Hadwiger’s conjecture for proper circular arc graphs
European Journal of Combinatorics, 2009 18 pages, 2 ...
Naveen Belkale, L. Sunil Chandran
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The Branch-Width of Circular-Arc Graphs [PDF]
, 2006 We prove that the branch-width of circular-arc graphs can be computed in polynomial time.
Mazoit, Frédéric, Frédéric Mazoit
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Recognizing H-Graphs - Beyond Circular-Arc Graphs. [PDF]
, 2023 In 1992 Biró, Hujter and Tuza introduced, for every fixed connected graph H, the class of H-graphs, defined as the intersection graphs of connected subgraphs of some subdivision of H. Such classes of graphs are related to many known graph classes: for example, K2-graphs coincide with interval graphs, K3-graphs with circular-arc graphs, the union of T ...
Deniz Agaoglu Çagirici +7 more
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Paths in interval graphs and circular arc graphs
Discrete Mathematics, 1993 Interval graphs and circular arc graphs are intersection graphs of intervals on a line resp. of arcs on a circle. We give polynomial-time algorithms for several path cover problems in such graphs, e.g. for finding a Hamiltonian path in a circular arc graph.
Damaschke, Peter
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