Finding and listing induced paths and cycles

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)+k⋅ck(G)) time, where pk(G), respectively, ck(G), are the num...

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Bibliographic Details
Published in:Discrete Applied Mathematics 2013-03, Vol.161 (4-5), p.633-641
Main Authors: Hoàng, Chính T., Kamiński, Marcin, Sawada, Joe, Sritharan, R.
Format: Article
Language:English
Subjects:
Algorithms
Brittleness
Graph algorithm
Graphs
Induced cycle
Induced path
Lists
Mathematical analysis
Recognition
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Summary: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)+k⋅ck(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!!⋅m(k−1)/2) if k is odd, and O(k!!⋅nm(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.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2012.01.024