Recognition of some perfectly orderable graph classes

Authors:
Elaine M. Eschen;Julie L. Johnson;Jeremy P. Spinrad;R. Sritharan
Affiliations:
Lane Department of Computer Science and Electrical Engineering, West Virginia University, P.O. Box 6109, Morgantown, WV;Computer Science Department, Vanderbilt University, Nashville, TN;Computer Science Department, Vanderbilt University, Nashville, TN;Computer Science Department, The University of Dayton, Dayton, OH
Venue:
Discrete Applied Mathematics
Year:
2003

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Abstract

This paper presents new algorithms for recognizing several classes of perfectly orderable graphs. Bipolarizable and P4-simplicial graphs are recognized in O(n3.376) time, improving the previous bounds of O(n4) and O(n5), respectively. Brittle and semi-simplicial graphs are recognized in O(n3) time using a randomized algorithm, and O(n3 log2n) time if a deterministic algorithm is required. The best previous time bound for recognizing these classes of graphs is O(m2). Welsh-Powell opposition graphs are recognized in O(n3) time, improving the previous bound of O(n4). HHP-free graphs and maxibrittle graphs are recognized in O(mn) and O(n3.376) time, respectively.