The packing chromatic number of hypercubes

被引：20
|
作者：
Torres, Pablo [1 ,2 ]
Valencia-Pabon, Mario [3 ]
机构：
[1] Univ Nacl Rosario, RA-2000 Rosario, Santa Fe, Argentina
[2] Consejo Nacl Invest Cient & Tecn, Rosario, Santa Fe, Argentina
[3] Univ Paris 13, Sorbonne Paris Cite, LIPN, CNRS UMR7030, F-93430 Villetaneuse, France
来源：
DISCRETE APPLIED MATHEMATICS | 2015年 / 190卷
关键词：
Packing chromatic number; Upper bound; Hypercube graphs; HEXAGONAL LATTICE; DISTANCE GRAPHS; COLORINGS; PRODUCT;
D O I：
10.1016/j.dam.2015.04.006
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The packing chromatic number chi(rho), (G) of a graph G is the smallest integer k needed to proper color the vertices of G in such a way that the distance in G between any two vertices having color i be at least i+1. Goddard et al. (2008) found an upper bound for the packing chromatic number of hypercubes Q(n). Moreover, they compute chi(rho), (Q(n)) for n <= 5 leaving as an open problem the remaining cases. In this paper, we obtain a better upper bound for chi(rho)(Q(n)) and we improve the lower bounds for chi(rho) (Q(n)) for 6 <= n <= 11. In particular we compute the exact value of chi(rho)(Q(n)) for 6 <= n <= 8. (C) 2015 Elsevier B.V. All rights reserved.
引用
收藏
页码：127 / 140
页数：14
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