Abstract

This paper presents new algorithms for recognizing several classes of perfectly orderable graphs. Bipolarizable and P 4-simplicial graphs are recognized in O( n 3.376) time, improving the previous bounds of O( n 4) and O( n 5), respectively. Brittle and semi-simplicial graphs are recognized in O( n 3) time using a randomized algorithm, and O(n 3 log 2n) time if a deterministic algorithm is required. The best previous time bound for recognizing these classes of graphs is O( m 2). Welsh–Powell opposition graphs are recognized in O( n 3) time, improving the previous bound of O( n 4). HHP-free graphs and maxibrittle graphs are recognized in O( mn) and O( n 3.376) time, respectively.

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