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

作者：Nikolopoulos Stavros D^*; Papadopoulos Charis

来源：Graphs and Combinatorics, 2011, 27(4): 557-565.

DOI：10.1007/s00373-010-0983-0

• Weakly quasi-threshold graphs
• Cographs
• Forbidden induced subgraphs
• Recognition
• Linear-time algorithms

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 quasi-threshold graphs coincides with the class of {P(4), co-(2P(3))}-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.

• 出版日期2011-7