Recognition of probe cographs and partitioned probe distance hereditary graphs

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Abstract

Given a class of graphs g, a graph G is a probe graph of g if its vertices can be partitioned into two sets ℙ (the probes) and ℕ (nonprobes), where ℕ is an independent set, such that G can be embedded into a graph of g by adding edges between certain vertices of ℕ. If the partition of the vertices into probes and nonprobes is part of the input, then we call the graph a partitioned probe graph of g. We give the first polynomial-time algorithm for recognizing partitioned probe distance-hereditary graphs. By using a novel data structure for storing a multiset of sets of numbers, the running time of this algorithm is O(n 2), where n is the number of vertices of the input graph. We also show that the recognition of both partitioned and unpartitioned probe cographs can be done in O(n 2) time. © Springer-Verlag Berlin Heidelberg 2006.

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Chandler, D. B., Chang, M. S., Kloks, T., Liu, J., & Peng, S. L. (2006). Recognition of probe cographs and partitioned probe distance hereditary graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4041 LNCS, pp. 267–278). Springer Verlag. https://doi.org/10.1007/11775096_25

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