A new upper bound for the chromatic number of a graph
Discussiones Mathematicae Graph Theory, Tome 27 (2007) no. 1, p. 137.

Voir la notice de l'article dans European Digital Mathematics Library

Let G be a graph of order n with clique number ω(G), chromatic number χ(G) and independence number α(G). We show that χ(G) ≤ [(n+ω+1-α)/2]. Moreover, χ(G) ≤ [(n+ω-α)/2], if either ω + α = n + 1 and G is not a split graph or α + ω = n - 1 and G contains no induced K ω + 3 - C ₅ .
Classification : 05C15, 05C69
Mots-clés : Vertex colouring, chromatic number, upper bound, vertex colouring, chromatic number upper bound, clique number 
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Ingo Schiermeyer. A new upper bound for the chromatic number of a graph. Discussiones Mathematicae Graph Theory, Tome 27 (2007) no. 1, p. 137. https://geodesic-test.mathdoc.fr/item/DMGT_2007__27_1_270707/