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Zero-Free Intervals of Chromatic Polynomials of Mixed Hypergraphs

Author

Listed:
  • Ruixue Zhang

    (School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China)

  • Fengming Dong

    (National Institute of Education, Nanyang Technological University, Singapore 637616, Singapore)

  • Meiqiao Zhang

    (National Institute of Education, Nanyang Technological University, Singapore 637616, Singapore)

Abstract

A mixed hypergraph H is a triple ( X , C , D ) , where X is a finite set and each of C and D is a family of subsets of X . For any positive integer λ , a proper λ -coloring of H is an assignment of λ colors to vertices in H such that each member in C contains at least two vertices assigned the same color and each member in D contains at least two vertices assigned different colors. The chromatic polynomial of H is the graph-function counting the number of distinct proper λ -colorings of H whenever λ is a positive integer. In this article, we show that chromatic polynomials of mixed hypergraphs under certain conditions are zero-free in the intervals ( − ∞ , 0 ) and ( 0 , 1 ) , which extends known results on zero-free intervals of chromatic polynomials of graphs and hypergraphs.

Suggested Citation

  • Ruixue Zhang & Fengming Dong & Meiqiao Zhang, 2022. "Zero-Free Intervals of Chromatic Polynomials of Mixed Hypergraphs," Mathematics, MDPI, vol. 10(2), pages 1-11, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:2:p:193-:d:720589
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