Equitable edge-colorings of K_(n,n) with restriction
Xia Zhang · Journal of Shandong University · 2005
Given a graph G and a positive integer r, let f e_r(G) denote the largest number of colors that can be used in a coloring of E(G) so that each vertex is incident with at most r colors, and that the color classes on the incident edges differ by at most 1 in size. For all positive integers n and r, a lower bound and an upper bound on f e_r(K_ n,n) are obtained. When r|n or r equal to 2,3 or n-1 , f e_r(K_ n,n) are determined exactly.