S. Wang, L. Xiong
On the independence number of traceable 2-connected claw-free graphs
Discussiones Mathematicae Graph Theory
Received 13.09.2016, Revised 12.12.2017, Accepted 30.12.2017, doi: 10.7151/dmgt.2113
A well-known theorem by Chvátal-Erdös [ A note on Hamilton circuits, Discrete Math. 2 (1972) 111--135] states that if the independence number of a graph G is at most its connectivity plus one, then G is traceable. In this article, we show that every 2-connected claw-free graph with independence number α(G)≤ 6 is traceable or belongs to two exceptional families of well-defined graphs. As a corollary, we also show that every 2-connected claw-free graph with independence number α(G)≤ 5 is traceable.
traceability, independence number, matching number, trail,