Chromatic polynomials of some sunflower mixed hypergraphs

Contributions to Discrete Mathematics

Julian D Allagan

关键词: Mathematics;    Math;    Discrete;   

学科分类：社会科学、人文和艺术（综合）

来源: University of Calgary * Department of Mathematics and Statistics

【 摘 要 】

The theory of mixed hypergraphs coloring has been first introduced by Voloshin in 1993 and it has been growing ever since. The proper coloring of a mixed hypergraph H =(X; C;D) is the coloring of the vertex set X so that no D-hyperedge is monochromatic and no C-hyperedge is polychromatic. A mixed hypergraph with hyperedges of type D, C or B is commonly known as a D-, C-, or B-hypergraph respectively, whereB = C = D. D-hypergraph colorings are the classic hypergraph colorings which have been widely studied. The chromatic polynomial P(H;) of a mixed hypergraph H is thefunction that counts the number of proper -colorings, which are mappings. Recently, Walter published [15] someresults concerning the chromatic polynomial of some non-uniform D-sunflower. In this paper, we present an alternative proof of his result and extend his formula to thoseof non-uniform C-sunflowers and B-sunflowers. Some results of a new but related member of sunflowers are also presented.

【 授权许可】

Unknown