Powers of asteroidal triple-free graphs with applications

Jou Ming Chang, Chin Wen Ho, Ming Tat Ko

研究成果: 雜誌貢獻期刊論文同行評審

14 引文 斯高帕斯(Scopus)


An asteroidal triple is an independent set of three vertices in a graph such that every two of them are joined by a path avoiding the closed neighborhood of the third. Graphs without asteroidal triples are called AT-free graphs. In this paper, we show that every AT-free graph admits a vertex ordering that we call a 2-cocomparability ordering. The new suggested ordering generalizes the cocomparability ordering achievable for cocomparability graphs. According to the property of this ordering, we show that every proper power Gk (k ≥ 2) of an AT-free graph G is a cocomparability graph. Moreover, we demonstrate that our results can be exploited for algorithmic purposes on AT-free graphs.

頁(從 - 到)161-173
期刊Ars Combinatoria
出版狀態已出版 - 4月 2003


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