INTERFERENCE PATTERNS IN REGULAR GRAPHS WITH BIJECTIVE COLORINGS.

Let gd(n) be the set of d-regular simple graphs with n vertices, and for G = (V, E) in gd(n) let f : → {1, 2, . . . , n} be a objective coloring of the vertices of G. Also let α denote an interference parameter in {0, 1,. . . ,n - 1}, and define the interference number of f with respect to G and α as the number of edges {u, v} in E for which min{/f(u) - f(v)\,n - f(u) - f(v)\} < α. We consider two interference number problems for feasible (n, α, d). The first is to specify a G E and an f for which the interference number is as small as possible. The second is to determine a G &epsiv; gd(n) whose minimum interference number over all f is as large as possible. A previous paper completely solves both problems for d = 2. The present paper solves the first problem for all d ≥ 3 and obtains partial results for the second problem for d ≥ 3 that focus on interference-minimizing f's when G consists of disjoint copies of Kd+1. [ABSTRACT FROM AUTHOR]