Geodesic
On graphs G for which both g and G̅ are claw-free
Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 3, pp. 267-272.

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Let G be a graph with |V(G)| ≥ 10. We prove that if both G and G̅ are claw-free, then minΔ(G), Δ(G̅) ≤ 2. As a generalization of this result in the case where |V(G)| is sufficiently large, we also prove that if both G and G̅ are K_1,t-free, then minΔ(G),Δ(G̅) ≤ r(t- 1,t)-1 where r(t-1,t) is the Ramsey number.
Keywords: claw-free, complement, maximum degree 
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Fujita, Shinya. On graphs G for which both g and G̅ are claw-free. Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 3, pp. 267-272. http://geodesic.mathdoc.fr/item/DMGT_2005_25_3_a5/

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