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Star chromatic indices of complete graphs.
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%I #12 May 15 2018 06:42:39

%S 0,1,3,5,9,12,14,14,18

%N Star chromatic indices of complete graphs.

%C The star chromatic index of a graph is the minimum number of colors needed to color the edges of a graph such that adjacent edges receive different colors and that on every path and cycle on four edges there are at least three different colors. The values a(n) are the star chromatic indices of the complete graph K_n. For the complete graph K_n, Dvořák, Mohar and Šámal conjectured that the star chromatic index is linear in n. For now, only the bounds up to n=9 are known. For n=10, the index is between 20 and 22.

%H Z. Dvořák, B. Mohar and R. Šámal, <a href="https://arxiv.org/abs/1011.3376">Star chromatic index</a>, arXiv:1011.3376 [math.CO],

%H Z. Dvořák, B. Mohar and R. Šámal, <a href="https://doi.org/10.1002/jgt.21644">Star chromatic index</a>, J. Graph Theory 72 (2013), 313-326.

%K nonn,hard

%O 1,3

%A _Borut Lužar_, May 14 2018