Upper bound for the number of spanning forests of regular graphs

Open Access
Authors
Publication date 05-2023
Journal European Journal of Combinatorics
Article number 103677
Volume | Issue number 110
Number of pages 12
Organisations
  • Faculty of Science (FNWI) - Korteweg-de Vries Institute for Mathematics (KdVI)
Abstract

We show that if G is a d–regular graph on n vertices, then the number of spanning forests F(G) satisfies F(G)≤dn. The previous best bound due to Kahale and Schulman gave (d+1/2+O(1/d))n. We also have the more precise conjecture that F(G)1/n≤[Formula presented].If this conjecture is true, then the expression on the right hand side is the best possible.

Document type Article
Language English
Published at https://doi.org/10.1016/j.ejc.2022.103677
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