Geodesic
A NOTE ON UPPER BOUND FOR CHROMATIC\\ NUMBER OF A GRAPH
Acta mathematica Universitatis Comenianae, Tome 71 (2002) no. 1 
L. Stacho. A NOTE ON UPPER BOUND FOR CHROMATIC\\
NUMBER OF A GRAPH. Acta mathematica Universitatis Comenianae, Tome 71 (2002) no. 1. http://geodesic.mathdoc.fr/item/AMUC_2002_71_1_a0/
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     author = {L. Stacho},
     title = {A {NOTE} {ON} {UPPER} {BOUND} {FOR} {CHROMATIC\\
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     journal = {Acta mathematica Universitatis Comenianae},
     year = {2002},
     volume = {71},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2002_71_1_a0/}
}
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NUMBER OF A GRAPH
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NUMBER OF A GRAPH
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Voir la notice de l'article provenant de la source Comenius University

Let \( G \) be a graph and let \( s \) be the maximum number of vertices of the same degree, each at least \( (\Delta (G)+2)/2 \), where \( \Delta \left( G\right) \) is the maximum degree in \( G \). We show that the chromatic number \( \chi \left( G\right) \leq \left\lceil \frac s s+1 \left( \Delta \left( G\right) +2\right) \right\rceil \).