2014/02/12 by Stefan Glock, Glock, Stefan
Computer Science · Mathematics · #05C15 #05C22 #05C72 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #math.CO #msc:05C15 #msc:05C22 #msc:05C72
paper · pdf · doi:10.48550/arxiv.1402.2916
arxiv created 2014/02/12 · openalex publication_date 2014/02/12 · arxiv updated 2014/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Our motivation is the question of how similar the f-colouring problem is to the classic edge-colouring problem, particularly with regard to graph parameters. In 2010, Zhang, Yu, and Liu gave a new description of the f-matching polytope and derived a formula for the fractional f-chromatic index, stating that the fractional f-chromatic index equals the maximum of the fractional maximum f-degree and the fractional f-density. Unfortunately, this formula is incorrect. We present counterexamples for both the description of the f-matching polytope and the formula for the fractional f-chromatic index. Finally, we prove a short lemma concerning the generalization of Goldberg's conjecture.