A note on module-composed graphs
Abstract
In this paper we consider module-composed graphs, i.e. graphs which can be defined by a sequence of one-vertex insertions v_1,...,v_n, such that the neighbourhood of vertex v_i, 2<= i<= n, forms a module (a homogeneous set) of the graph defined by vertices v_1,..., v_{i-1}. We show that module-composed graphs are HHDS-free and thus homogeneously orderable, weakly chordal, and perfect. Every bipartite distance hereditary graph, every (co-2C_4,P_4)-free graph and thus every trivially perfect graph is module-composed. We give an O(|V_G|(|V_G|+|E_G|)) time algorithm to decide whether a given graph G is module-composed and construct a corresponding module-sequence. For the case of bipartite graphs, module-composed graphs are exactly distance hereditary graphs, which implies simple linear time algorithms for their recognition and construction of a corresponding module-sequence.
Cite
@article{arxiv.0705.1521,
title = {A note on module-composed graphs},
author = {Frank Gurski},
journal= {arXiv preprint arXiv:0705.1521},
year = {2007}
}