On 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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For a positive integer k, a k-packing in a graph G is a subset A of vertices such that the distance between any two distinct vertices from A is more than k. The packing chromatic number of G is the smallest integer m such that the vertex set of G can be partitioned as V1, V2, . . . , Vm where Vi is an i-packing for each i. It is proved that the planar triangular lattice T and the 3-dimensional ...
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ژورنال
عنوان ژورنال: Electronic Notes in Discrete Mathematics
سال: 2013
ISSN: 1571-0653
DOI: 10.1016/j.endm.2013.10.041