2020/10/10 by Jin‐Yi Cai, Cai, Jin-Yi, Artem Govorov +1 · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Advanced Topology and Set Theory #Computational Complexity (cs.CC) #FOS: Computer and information sciences #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2010.04910
openalex publication_date 2020/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove #P-completeness results for counting edge colorings on simple graphs. These strengthen the corresponding results on multigraphs from [4]. We prove that for any κ≥ r ≥ 3 counting κ-edge colorings on r-regular simple graphs is #P-complete. Furthermore, we show that for planar r-regular simple graphs where r ∈ \3, 4, 5\ counting edge colorings with \kappa colors for any κ≥ r is also #P-complete. As there are no planar r-regular simple graphs for any r > 5, these statements cover all interesting cases in terms of the parameters (κ, r).