Kruskalian graphs k-cographs

Authors:
Ling-Ju Hung;Ton Kloks
Affiliations:
National Chung Cheng University, Min-Hsiung, Chia-Yi, Taiwan;National Chung Cheng University, Min-Hsiung, Chia-Yi, Taiwan
Venue:
CATS '10 Proceedings of the Sixteenth Symposium on Computing: the Australasian Theory - Volume 109
Year:
2010

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Abstract

A class of graphs is Kruskalian if Kruskal's theorem on a well-quasi-ordering of finite trees provides a finite characterization in terms of forbidden induced subgraphs. Let k be a natural number. A graph is a k-cograph if its vertices can be colored with colors from the set {1, ..., k} such that for every nontrivial subset of vertices W there exists a partition {W1,W2} into nonempty subsets such that either no vertex of W1 is adjacent to a vertex of W2 or, such that there exists a permutation π ε Sk such that vertices with color i in W1 are adjacent exactly to the vertices with color π(i) in W2, for all i ε {1, ..., k}. We prove that k-cographs are Kruskalian. We show that k-cographs have bounded rankwidth and that they can be recognized in O(n3) time.