Independent sets near the lower bound in bounded degree graphs
Discrete Mathematics
2019-11-05 v2 Combinatorics
Abstract
By Brook's Theorem, every n-vertex graph of maximum degree at most Delta >= 3 and clique number at most Delta is Delta-colorable, and thus it has an independent set of size at least n/Delta. We give an approximate characterization of graphs with independence number close to this bound, and use it to show that the problem of deciding whether such a graph has an indepdendent set of size at least n/Delta+k has a kernel of size O(k).
Keywords
Cite
@article{arxiv.1609.09134,
title = {Independent sets near the lower bound in bounded degree graphs},
author = {Zdenek Dvorak and Bernard Lidicky},
journal= {arXiv preprint arXiv:1609.09134},
year = {2019}
}
Comments
19 pages, 6 figures; fixes an error pointed out by Andrea Munaro