arXiv Analytics

Sign in

arXiv:1908.06300 [cs.DM]AbstractReferencesReviewsResources

The stable set problem in graphs with bounded genus and bounded odd cycle packing number

Michele Conforti, Samuel Fiorin, Tony Huynh, Gwenaël Joret, Stefan Weltge

Published 2019-08-17Version 1

Consider the family of graphs without $ k $ node-disjoint odd cycles, where $ k $ is a constant. Determining the complexity of the stable set problem for such graphs $ G $ is a long-standing problem. We give a polynomial-time algorithm for the case that $ G $ can be further embedded in a (possibly non-orientable) surface of bounded genus. Moreover, we obtain polynomial-size extended formulations for the respective stable set polytopes. To this end, we show that $2$-sided odd cycles satisfy the Erd\H{o}s-P\'osa property in graphs embedded in a fixed surface. This extends the fact that odd cycles satisfy the Erd\H{o}s-P\'osa property in graphs embedded in a fixed orientable surface (Kawarabayashi & Nakamoto, 2007). Eventually, our findings allow us to reduce the original problem to the problem of finding a minimum-cost non-negative integer circulation of a certain homology class, which turns out to be efficiently solvable in our case.

Related articles: Most relevant | Search more
arXiv:1911.01478 [cs.DM] (Published 2019-11-04)
Persistency of Linear Programming Formulations for the Stable Set Problem
arXiv:2205.03757 [cs.DM] (Published 2022-05-08)
Cover time of graphs with bounded genus
arXiv:1004.4484 [cs.DM] (Published 2010-04-26)
Determining Edge Expansion and Other Connectivity Measures of Graphs of Bounded Genus