Achromatic number of K5×Kn for large n
نویسندگان
چکیده
منابع مشابه
Concerning the achromatic number of graphs
The achromatic number of a graph G is the largest number of colors that can be assigned to the vertices of G so that (i) adjacent vertices are assigned different colors, and (ii) any two different colors are assigned to some pair of adjacent vertices. We study the achromatic number from the point of view of computational complexity. We show that, for each fixed integer n, there is an algorithm ...
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The achromatic number α of a graph is the largest number of colors that can be assigned to its vertices such that adjacent vertices have different color and every pair of different colors appears on the end vertices of some edge. We estimate the achromatic number of Kneser graphs K(n, k) and determine α(K(n, k)) for some values of n and k. Furthermore, we study the achromatic number of some geo...
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The achromatic number of a nite graph G, (G), is the maximum number of independent sets into which the vertex set may be partitioned, so that between any two parts there is at least one edge. For an m-dimensional hypercube P m 2 we prove: There exist constants 0 < c 1 < c 2 , independent of m, such that
متن کاملAn Improved Approximation of the Achromatic Number on Bipartite Graphs
The achromatic number of a graph G = (V,E) with | V |= n vertices is the largest number k with the following property: the vertices of G can be partitioned into k independent subsets {Vi}1≤i≤k such that for every distinct pair of subsets Vi, Vj in the partition, there is at least one edge in E that connects these subsets. We describe a greedy algorithm that computes the achromatic number of a b...
متن کاملOn the achromatic number of the Cartesian product G1×G2
We study the achromatic number of the Cartesian product of graphs G 1 and G 2 and obtain the following results: (i) maXl<t<rn min{l mn J, t(m + n-1)-t 2 + I}
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2001
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(00)00399-x