Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776976 | Discrete Mathematics | 2017 | 8 Pages |
Abstract
We determine the maximum number of edges that a claw-free graph can have, when its maximum degree and matching number are bounded. This is a famous problem that has been studied on general graphs, and for which there is a tight bound. The graphs achieving this bound contain in most cases an induced copy of K1,3, the claw, which motivates studying the question on claw-free graphs. Note that on general graphs, if one of the mentioned parameters is not bounded, then there is no upper bound on the number of edges. We show that on claw-free graphs, bounding the matching number is sufficient for obtaining an upper bound on the number of edges. The same is not true for the degree, as a long path is claw-free. We give exact tight formulas for both when only the matching number is bounded and when both parameters are bounded. We also construct claw-free graphs whose edge numbers match the given bounds.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Cemil Dibek, Tınaz Ekim, Pinar Heggernes,