The packing chromatic number of hypercubes
نویسندگان
چکیده
منابع مشابه
On the packing chromatic number of hypercubes
The packing chromatic number χρ(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. [8] found an upper bound for the packing chromatic number of hypercubes Qn. Moreover, they compute χρ(Qn) for n ≤ 5 leaving as an open problem the remaining cases. In this p...
متن کاملThe packing chromatic number of hypercubes
The packing chromatic number χρ(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. [9] found an upper bound for the packing chromatic number of hypercubes Qn. Moreover, they compute χρ(Qn) for n ≤ 5 leaving as an open problem the remaining cases. In this...
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The packing chromatic number χρ(G) of a graph G is the smallest integer k for which there exists a mapping π : V (G) −→ {1, 2, ..., k} such that any two vertices of color i are at distance at least i+ 1. In this paper, we compute the packing chromatic number for enhanced hypercubes.
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The packing chromatic number χρ(G) of a graphG is the smallest integer k such that the vertex set of G can be partitioned into sets Vi, i ∈ [k], where each Vi is an i-packing. In this paper, we investigate for a given triple (a, b, c) of positive integers whether there exists a graph G such that ω(G) = a, χ(G) = b, and χρ(G) = c. If so, we say that (a, b, c) is realizable. It is proved that b =...
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The packing chromatic number (G) of a graph G is the smallest integer k such that vertices of G can be partitioned into disjoint classes X1; :::; Xk where vertices in Xi have pairwise distance greater than i. We study the packing chromatic number of in nite distance graphs G(Z; D), i.e. graphs with the set Z of integers as vertex set and in which two distinct vertices i; j 2 Z are adjacent if a...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2015
ISSN: 0166-218X
DOI: 10.1016/j.dam.2015.04.006