Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4647124 | Discrete Mathematics | 2016 | 6 Pages |
Abstract
In this paper we consider the existence of (s,p)-equitable block-colorings of 4-cycle decompositions of KvâF, where F is a 1-factor of Kv. In such colorings, the 4-cycles are colored with s colors in such a way that, for each vertex u, the 4-cycles containing u are colored with p colors so that the number of such 4-cycles of each color is within one of the number of such 4-cycles of each of the other pâ1 colors. Of primary interest is settling the values of Ïpâ²(v) and ÏÌpâ²(v), namely the least and greatest values of s for which there exists such a block-coloring of some 4-cycle decomposition of KvâF. In this paper, several general results are established, both existence and non-existence theorems. These are then used to find, for all possible values of v, the values of Ïpâ²(v) when pâ{2,3,4} and ÏÌ2â²(v), and to provide good upper bounds on ÏÌ3â²(v).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Shanhai Li, C.A. Rodger,