Neighborhood intersections and Hamiltonicity in almost claw-free graphs

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Let G be a graph. The partially square graph G* of G is a graph obtained from G by adding edges uv satisfying the conditions uvgE(G), and there is some w E N(u) C\ N(v), such that N(w)CN(u)UN(v)U{u,v}. Let t > 1 be an integer and YÇ F(G), denote n(Y) = \{ve K(G)| min,.<E Y{d\slc(v,y)}<2}|, I,(G) = {Z\Z is an independent set of G,\Z\ = t}. In this paper, we show that a k-connected almost claw-free graph with A->2 is hainiltonian if J.ez </(z)n(Z)k in G for each Z∈/I+i(G*), thereby solving a conjecture proposed by Broersma, Ryjâcek and Schiermeyer. Zhang's result is also generalized by the new result. ©2002 Elsevier Science B.V. All rights reserved.




Zhan, M. (2002). Neighborhood intersections and Hamiltonicity in almost claw-free graphs. Discrete Mathematics, 243(1–3), 171–185.

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