Finding and listing induced paths and cycles

Authors:
ChíNh T. HoíNg;Marcin KamińSki;Joe Sawada;R. Sritharan
Affiliations:
Physics and Computer Science, Wilfrid Laurier University, Canada;Algorithms Research Group, Département d'Informatique, Université Libre de Bruxelles O8.114, CP 212, Bvd. du Triomphe, 1050 Bruxelles, Belgium;School of Computer Science, University of Guelph, Canada;Computer Science Department, The University of Dayton, Dayton, OH 45469, United States
Venue:
Discrete Applied Mathematics
Year:
2013

Citing 8
Cited 0

Matrix multiplication via arithmetic progressions

Journal of Symbolic Computation - Special issue on computational algebraic complexity
On the complexity of recognizing perfectly orderable graphs

Discrete Mathematics
Recognizing brittle graphs: remarks on a paper of Hoa`ng and Khouzam

Discrete Applied Mathematics
Finding large holes

Information Processing Letters
Recognition of some perfectly orderable graph classes

Discrete Applied Mathematics
A Note on Quasi-triangulated Graphs

SIAM Journal on Discrete Mathematics
Recognizing quasi-triangulated graphs

Discrete Applied Mathematics
On graphs without a C4 or a diamond

Discrete Applied Mathematics

Quantified Score

Hi-index	0.04

Visualization

Abstract

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 P"3's in O(m^1^.^5+p"3(G)) time, and for k=4 all P"k's in O(n^k^-^1+p"k(G)+k@?c"k(G)) time, where p"k(G), respectively, c"k(G), are the number of P"k's, respectively, C"k's, of a graph G. We also provide an algorithm to find a P"k, 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.