منابع مشابه
Acyclic and Star Colorings of Cographs
An acyclic coloring of a graph is a proper vertex coloring such that the union of any two color classes induces a disjoint collection of trees. The more restricted notion of star coloring requires that the union of any two color classes induces a disjoint collection of stars. We prove that every acyclic coloring of a cograph is also a star coloring and give a linear-time algorithm for finding a...
متن کاملApproximating Treewidth and Pathwidth of some Classes of Perfect Graphs
In this paper we discuss the problem of finding approximations for the treewidth and pathwidth of cotriangulated graphs, convex graphs, permutation graphs and of cocomparability graphs. For a cotriangulated graph, of which the treewidth is at most k, the pathwidth is at most 3k + 4 and we show there exists an O( n2 ) algorithm finding a path-decomposition with width at most 3k + 4. For convex g...
متن کاملOn the treewidth and pathwidth of permutation graphs
In this paper we discuss the problem of finding the treewidth and pathwidth of permutation graphs. If G[7r] is a permutation graph with treewidth k, then we show that the pathwidth of G[7r] is at most 2k, and we give an algorithm which constructs a path-decomposition with width at most 2k in time O( nk). We assume that the permutation 7r is given. For permutation graphs of which the treewidth i...
متن کاملTREEWIDTH and PATHWIDTH parameterized by vertex cover
After the number of vertices, Vertex Cover is the largest of the classical graph parameters and has more and more frequently been used as a separate parameter in parameterized problems, including problems that are not directly related to the Vertex Cover. Here we consider the TREEWIDTH and PATHWIDTH problems parameterized by k, the size of a minimum vertex cover of the input graph. We show that...
متن کاملCyclewidth: an Analogy of Treewidth
In this work we study cyclewidth, a generalization of treewidth and pathwidth to cycles. Although treewidth and pathwidth have been extensively studied, cyclewidth has only been mentioned in a single paper, to the best of the author’s knowledge. We prove that the decision problem of determining whether the cyclewidth of a graph is at most k is NP-complete. We also present an algorithm for findi...
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تاریخ انتشار 1990