Geodesic
On the Independence Number of Traceable 2-Connected Claw-Free Graphs
Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 4, pp. 925-937

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A well-known theorem by Chvátal-Erdőos [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.
Keywords: traceability, independence number, matching number, trail, closure 
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Wang, Shipeng; Xiong, Liming. On the Independence Number of Traceable 2-Connected Claw-Free Graphs. Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 4, pp. 925-937. http://geodesic.mathdoc.fr/item/DMGT_2019_39_4_a12/