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<p>Radchenko and Villegas characterized the chordal graphs by the inverse of their independence polynomials being Horn hypergeometric series in (Bull Lond Math Soc 53(6):1834-1848, 2021). In this paper, we reprove their result using some elementary combinatorial methods. Our proof is different from their proof, and it is based on the connection between the inverse of the multi-variate independence polynomials and the multi-colored chromatic polynomials of graphs, established in 2018 by Arunkumar et al.</p>

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On the characterization of chordal graphs using Horn hypergeometric series

  • 期刊论文

  • 发表日期：

    2025年1月6日

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  • Dipnit Biswas,
  • Irfan Habib,
  • R. Venkatesh

摘要

Radchenko and Villegas characterized the chordal graphs by the inverse of their independence polynomials being Horn hypergeometric series in (Bull Lond Math Soc 53(6):1834-1848, 2021). In this paper, we reprove their result using some elementary combinatorial methods. Our proof is different from their proof, and it is based on the connection between the inverse of the multi-variate independence polynomials and the multi-colored chromatic polynomials of graphs, established in 2018 by Arunkumar et al.