The b-chromatic number of powers of cyclesReport as inadecuate




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1 Faculty of Informatics-Mathematics Dresden

Abstract : A b-coloring of a graph G by k colors is a proper vertex coloring such that each color class contains a color-dominating vertex, that is, a vertex having neighbors in all other k-1 color classes. The b-chromatic number χbG is the maximum integer k for which G has a b-coloring by k colors. Let Cnr be the rth power of a cycle of order n. In 2003, Effantin and Kheddouci established the b-chromatic number χbCnr for all values of n and r, except for 2r+3≤n≤3r. For the missing cases they presented the lower bound L:= min n-r-1,r+1+⌊ n-r-1 - 3⌋ and conjectured that χbCnr=L. In this paper, we determine the exact value on χbCnr for the missing cases. It turns out that χbCnr>L for 2r+3≤n≤2r+3+r-6 - 4.





Author: Anja Kohl -

Source: https://hal.archives-ouvertes.fr/



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