Independent sets near the lower bound in bounded degree graphs

Zdenek Dvorak, Bernard Lidicky

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).

Knowledge Graph

arrow_drop_up

Comments

Sign up or login to leave a comment