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A note on the chromatic number of the square of the Cartesian product of two cycles
Zehui Shao, Aleksander Vesel, 2013, short scientific article

Abstract: The square ▫$G^2$▫ of a graph ▫$G$▫ is obtained from ▫$G$▫ by adding edges joining all pairs of nodes at distance 2 in ▫$G$▫. In this note we prove that ▫$chi((C_mBox C_n)^2) le 6$ for $m, n ge 40$▫. This confirms Conjecture 19 stated in [É. Sopena, J. Wu, Coloring the square of the Cartesian product of two cycles, Discrete Math. 310 (2010) 2327-2333].
Keywords: matematika, teorija grafov, kromatično število, kartezični produkt, označevanje grafov, kvadrat grafa, mathematics, graph theory, chromatic number, Cartesian product, graph labeling, square if a graph
Published: 10.07.2015; Views: 713; Downloads: 66
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