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Finding and listing induced paths and cycles

par Hoàng, Chính T.;Kaminski, Marcin ;Sawada, Joe;Sritharan, R.
Référence Discrete applied mathematics, 161, 4-5, page (633-641)
Publication Publié, 2013-03

Article révisé par les pairs

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Résumé :

Many recognition problems for special classes of graphs and cycles can be reduced to finding and listing induced paths and cycles in a graph. We design algorithms to list all P3's in O(m1.5+p3(G)) time, and for k≥4 all Pk's in O(nk-1+ pk(G)+kṡck(G)) time, where pk(G), respectively, ck(G), are the number of Pk's, respectively, Ck's, of a graph G. We also provide an algorithm to find a Pk, k≥5, in time O(k!!ṡm(k-1)/2) if k is odd, and O(k!!ṡnm(k/2)-1) if k is even. As applications of our findings, we give algorithms to recognize quasi-triangulated graphs and brittle graphs. Our algorithms' time bounds are incomparable with previously known algorithms. © 2011 Elsevier B.V. All rights reserved.