In this paper we study the
-chromatic number of the cartesian product of two graphs. The
-chromatic number of a graph
is defined as the maximum number
of colors that can be used to color the vertices of
, such that we obtain a proper coloring and each color
has at least one representative
adjacent to a vertex of every color
, 1 ≦
. In this paper we get ρ(
) ≦ ρ(
+ 1) + Δ(
) + 1, when the girth of
is assumed to be greater than or equal to 7.
Farber, M., Hahn, G., Hell, P.
and Miller, D. J.
, Concerning the achromatic number of graphs,
J. Comb. Theory (B)40
(1986), 21–39. MR
Miller D. J. , 'Concerning the achromatic number of graphs' (1986) 40J. Comb. Theory (B): 21-39.
Miller D. J. Concerning the achromatic number of graphsJ. Comb. Theory (B)1986402139)| false