Zehui Shao (Author), Aleksander Vesel (Author)

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 ▫$\chi((C_m\Box C_n)^2) \le 6$ 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;

Data

Language: English
Year of publishing:
Typology: 1.03 - Short Scientific Article
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
UDC: 519.17
COBISS: 19836168 Link will open in a new window
ISSN: 0012-365X
Views: 446
Downloads: 23
Average score: 0 (0 votes)
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Other data

Secondary language: English
Secondary title: O kromatičnem številu kvadrata kartezičnega produkta dveh ciklov
URN: URN:SI:UM:
Type (COBISS): Not categorized
Pages: str. 999-1001
Volume: Vol. 313
Issue: iss. 9
Chronology: 2013
ID: 1477048