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We prove that every claw-free graph $G$ that doesn't contain a clique on $\Delta(G) \geq 9$ vertices can be $\Delta(G) - 1$ colored.
We show that the two distinct venices u and v of a 2-connected claw-free graph G of order n with minimun degree(n- 2)/3 are [7, n]-panconnected whenever both G-u and G-v are 2-connected.
M. Matthews and D. Sumner proved that if G is a 2-connected claw-free graph of order n, then c(G)\geq \min{2δ + 4, n}. In this paper, we prove that if G is a 2-connected claw-free graph on n venices, ...