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.
Cite
CITATION STYLE
Chang, J. M., Ho, C. W., & Ko, M. T. (1999). Lexbfs-ordering in asteroidal triple-free graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1741, pp. 163–172). Springer Verlag. https://doi.org/10.1007/3-540-46632-0_17
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