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Zero-free intervals of chromatic polynomials of mixed hypergraphs
Citation
Zhang, R., Dong, F., & Zhang, M. (2022). Zero-free intervals of chromatic polynomials of mixed hypergraphs. Mathematics, 10(2), 193. https://doi.org/10.3390/math10020193
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.
Date Issued
2022
Publisher
MDPI
Journal
Mathematics
Grant ID
12101347
ZR2021QA085
Funding Agency
Nanyang Technological University, Singapore
National Science Foundation of China
National Science Foundation of Shandong Province of China