Geodesic
On traceability and 2-factors in claw-free graphs
Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 1, pp. 55-71

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If G is a claw-free graph of sufficiently large order n, satisfying a degree condition σₖ > n + k² - 4k + 7 (where k is an arbitrary constant), then G has a 2-factor with at most k - 1 components. As a second main result, we present classes of graphs ₁,...,₈ such that every sufficiently large connected claw-free graph satisfying degree condition σ₆(k) > n + 19 (or, as a corollary, δ(G) > (n+19)/6) either belongs to ⋃ ⁸_i=1 _i or is traceable.
Keywords: traceability, 2-factor, claw, degree condition, closure 
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Fronček, Dalibor; Ryjáček, Zdeněk; Skupień, Zdzisław. On traceability and 2-factors in claw-free graphs. Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 1, pp. 55-71. http://geodesic.mathdoc.fr/item/DMGT_2004_24_1_a4/