منابع مشابه
Minimal vertex separators and new characterizations for dually chordal graphs
Many works related to dually chordal graphs, their cliques and neighborhoods were published. We will undertake a similar study but by considering minimal separators and their properties. Moreover we find new characterizations of dually chordal graphs.
متن کاملMinimal Separators in Intersection Graphs
In this report, we present the intersection graphs and describe the role they play in computations of treewidth. We introduce minimal triangulations, minimal separators, potential maximal cliques and blocks as the main tools for exact computation and approximation of that important graph parameter. The first chapter is an introduction to the intersection graph theory. We give all the necessary ...
متن کاملOn minimal vertex separators of dually chordal graphs: Properties and characterizations
Many works related to dually chordal graphs, their cliques and neighborhoods were published [1, 6]. We will undertake a similar study by considering minimal vertex separators and their properties instead. We find a necessary and sufficient condition for every minimal vertex separator to be contained in the closed neighborhood of a vertex and two major characterizations of dually chordal graphs ...
متن کاملMinimal separators in P4-sparse graphs
In this paper, we determine the minimal separators of P4-sparse graphs and establish bounds on their number. Specifically, we show that a P4-sparse graph G on n vertices and m edges has fewer than 2n/3 minimal separators of total description size at most 4m/3. The bound on the number of minimal separators is tight and is also tight for the class of cographs, a well known subclass of the P4-spar...
متن کاملGraphs with complete minimal k-vertex separators
G. A. Dirac characterized chordal graphs as those in which minimal vertex separators always induce complete subgraphs. I generalize a traditional (2-)vertex separator to a k-vertex separator — meaning a set S of vertices whose removal puts k independent vertices into k separate components. Generalizing Dirac’s theorem, the {P5, 2P3}-free chordal graphs are the graphs in which minimal k-separato...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1993
ISSN: 0024-3795
DOI: 10.1016/0024-3795(93)90378-2