Asymptotic number of edge-colored regular graphs

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Michael Borinsky, Chiara Meroni, Wiesmann, Maximilian
DOI: 10.48550/arxiv.2601.18994
Cited by: 0

Abstract

We prove a formula for the asymptotic number of edge-colored regular graphs with a prescribed set of allowed vertex-incidence structures. The formula depends on specific critical points of a polynomial encoding the vertex-incidences. As an application, we compute the expected number of proper $c$-edge-colorings of a large random $k$-regular graph.

Fields of Study & Subjects

Limits and Structures in Graph Theory Advanced Graph Theory Research Advanced Combinatorial Mathematics

Publication details

Journal / source
arXiv (Cornell University)
Publication date
26 January 2026
Document type
Preprint