Chromatic polynomials of some sunflower mixed hypergraphs
- ECSU Author/Contributor (non-ECSU co-authors, if there are any, appear on document)
- Julian A. D. Allagan , Associate Professor (Creator)
- Institution
- Elizabeth City State University (ECSU )
- Web Site: https://www.ecsu.edu/academics/library/index.html
Abstract: 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 ofthe 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-hypergraphrespectively where B = C = D. D-hypergraph colorings are the classichypergraph colorings which have been widely studied. The chro-matic polynomial P(H;) of a mixed hypergraph H is the function thatcounts the number of proper ??colorings, which are mappings f : X !f1; 2; : : : ; g. A sunfower (hypergraph) with l petals and a core S is a collection of sets e1; : : : ; el such that ei \ ej = S for all i 6= j. Recently, Walter published [14] some results concerning the chromatic polynomial of some non-uniform D-sunfower. In this paper, we present an alternative proof of his result and extend his formula to those of non-uniform C-sunowers and B-sunowers. Some results of a new but related member of sunfowers are also presented.
Chromatic polynomials of some sunflower mixed hypergraphs
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Created on 2/19/2023
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Additional Information
- Publication
- Language: English
- Date: 2010
- Keywords
- sunflowers, polynomials, mixed hypergraphs