A Simple Linear-Time Recognition Algorithm for Weakly Quasi-Threshold Graphs

13 years 5 months ago

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: Weakly quasi-threshold graphs form a proper subclass of the well-known class of cographs by restricting the join operation. In this paper we characterize weakly quasi-threshold graphs by a finite set of forbidden subgraphs: the class of weakly quasithreshold graphs coincides with the class of {P4, co-(2P3)}-free graphs. Moreover we give the first linear-time algorithm to decide whether a given graph belongs to the class of weakly quasi-threshold graphs, improving the previously known running time. Based on the simplicity of our recognition algorithm, we can provide certificates of membership (a structure that characterizes weakly quasi-threshold graphs) or non-membership (forbidden induced subgraphs) in additional O(n) time. Furthermore we give a linear-time algorithm for finding the largest induced weakly quasi-threshold subgraph in a cograph.

Stavros D. Nikolopoulos, Charis Papadopoulos

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