LexBFS-Ordering in Asteroidal Triple-Free Graphs

Authors:
Jou-Ming Chang;Chin-Wen Ho;Ming-Tat Ko
Affiliations:
-;-;-
Venue:
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
Year:
1999

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Abstract

In this paper, we study the metric property of LexBFS-ordering on AT-free graphs. Based on a 2-sweep LexBFS algorithm, we show that every AT-free graph admits a vertex ordering, called the strong 2-cocomparability ordering, that for any three vertices u ≺ v ≺ w in the ordering, if d(u, w) ≤ 2 then d(u, v) = 1 or d(v, w) ≤ 2. As an application of this ordering, we provide a simple linear time recognition algorithm for bipartite permutation graphs, which form a subclass of AT-free graphs.