Strongly Chordal and Chordal Bipartite Graphs Are Sandwich Monotone

摘要

A graph class is sandwich monotone if, for every pair of its graphs G_1 = (V, E_1) and G_2 = (V, E_2) with E_1 is contained in E_2, there is an ordering e_1,…, e_k; of the edges in E_2 E_1 such that G = (V, E_1 ∪ {e_1,…, e_i}) belongs to the class for every I between 1 and k. In this paper we show that strongly chordal graphs and chordal bipartite graphs are sandwich monotone, answering an open question by Bakonyi and Bono from 1997. So far, very few classes have been proved to be sandwich monotone, and the most famous of these are chordal graphs. Sandwich monotonicity of a graph class implies that minimal completions of arbitrary graphs into that class can be recognized and computed in polynomial time. For minimal completions into strongly chordal or chordal bipartite graphs no polynomial-time algorithm has been known. With our results such algorithms follow for both classes. In addition, from our results it follows that all strongly chordal graphs and all chordal bipartite graphs with edge constraints can be listed efficiently.