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 -free, then minΔ(G),Δ(G̅) ≤ r(t- 1,t)-1 where r(t-1,t) is the Ramsey number.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1280,
author = {Shinya Fujita},
title = {On graphs G for which both g and G are claw-free},
journal = {Discussiones Mathematicae Graph Theory},
volume = {25},
year = {2005},
pages = {267-272},
zbl = {1106.05081},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1280}
}
Shinya Fujita. On graphs G for which both g and G̅ are claw-free. Discussiones Mathematicae Graph Theory, Tome 25 (2005) pp. 267-272. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1280/
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