Results 281 to 290 of about 226,666 (311)
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Journal of Graph Theory, 1993
AbstractAn interval graph is said to be extremal if it achieves, among all interval graphs having the same number of vertices and the same clique number, the maximum possible number of edges. We give an intrinsic characterization of extremal interval graphs and derive recurrence relations for the numbers of such graphs.
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AbstractAn interval graph is said to be extremal if it achieves, among all interval graphs having the same number of vertices and the same clique number, the maximum possible number of edges. We give an intrinsic characterization of extremal interval graphs and derive recurrence relations for the numbers of such graphs.
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Combinatorica, 1988
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Separator Theorems for Interval Graphs and Proper Interval Graphs
2015C.L.Monma and V.K.Wei [1986, J. Comb. Theory, Ser-B, 41, 141-181] proposed a unified approach to characterize several subclasses of chordal graphs using clique separator. The characterizations so obtained are called separator theorems. Separator theorems play an important role in designing algorithms in subclasses of chordal graphs.
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Unit Interval Graphs of Open and Closed Intervals
Journal of Graph Theory, 2012AbstractWe give two structural characterizations of the class of finite intersection graphs of the open and closed real intervals of unit length. This class is a proper superclass of the well‐known unit interval graphs.
Dieter Rautenbach +1 more
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Weighted irredundance of interval graphs
Information Processing Letters, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Maw-Shang Chang +2 more
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2002
Summary: We introduce interval \(k\)-graphs, a family of restricted intersection graphs. The intersection model for interval \(k\)-graphs assigns each vertex to a unique interval in some copy of the real line, with two vertices adjacent whenever their corresponding intervals overlap and belong to distinct copies of \(\mathbb{R}\). Our work is motivated
Brown, David E. +2 more
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Summary: We introduce interval \(k\)-graphs, a family of restricted intersection graphs. The intersection model for interval \(k\)-graphs assigns each vertex to a unique interval in some copy of the real line, with two vertices adjacent whenever their corresponding intervals overlap and belong to distinct copies of \(\mathbb{R}\). Our work is motivated
Brown, David E. +2 more
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Characterizing interval graphs which are probe unit interval graphs
Discrete Applied Mathematics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Chordal graphs, interval graphs, and wqo
Journal of Graph Theory, 1998Let \(\preceq\) be the induced-minor relation. It is shown that, for every \(t\), all chordal graphs of clique number at most \(t\) are well-quasi-ordered by \(\preceq\). On the other hand, if the bound on the clique number is dropped, even the class of interval graphs is not well-quasi-ordered by \(\preceq\).
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Listing Chordal Graphs and Interval Graphs
2006We propose three algorithms for enumeration problems; given a graph G, to find every chordal supergraph (in Kn) of G, to find every interval supergraph (in Kn) of G, and to find every interval subgraph of G in Kn. The algorithms are based on the reverse search method.
Masashi Kiyomi +2 more
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2001
A bipartite graph with partitions \(P\) and \(C\) is called an interval bigraph, if there exists a family of intervals which associates each vertex of \(G=(V, E)\) with an interval, and for \(x,y \in V\) the edge between \(x\) and \(y\) is in \(E\) if the corresponding intervals intersect and at least one of \(x\) and \(y\) is in \(P\). After a lengthy
Brown, David E. +2 more
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A bipartite graph with partitions \(P\) and \(C\) is called an interval bigraph, if there exists a family of intervals which associates each vertex of \(G=(V, E)\) with an interval, and for \(x,y \in V\) the edge between \(x\) and \(y\) is in \(E\) if the corresponding intervals intersect and at least one of \(x\) and \(y\) is in \(P\). After a lengthy
Brown, David E. +2 more
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