Partition into triangles on bounded degree graphs

Authors:
Johan M. M. Van Rooij;Marcel E. Van Kooten Niekerk;Hans L. Bodlaender
Affiliations:
Department of Information and Computing Sciences, Utrecht University, Utrecht, The Netherlands;Department of Information and Computing Sciences, Utrecht University, Utrecht, The Netherlands;Department of Information and Computing Sciences, Utrecht University, Utrecht, The Netherlands
Venue:
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Year:
2011

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Abstract

We consider the PARTITION INTO TRIANGLES problem on bounded degree graphs. We show that this problem is polynomial time solvable on graphs of maximum degree three by giving a linear time algorithm. We also show that this problem becomes NP-complete on graphs of maximum degree four. Moreover, we show that there is no subexponential time algorithm for this problem on maximum degree four graphs unless the Exponential Time Hypothesis fails. However, the partition into triangles problem for graphs of maximum degree at most four is in many cases practically solvable as we give an algorithm for this problem that runs in O(1.02220n) time and linear space. In this extended abstract, we will only give an O(1.02445n) time algorithm.