The Fractional Chromatic Number of \(\boldsymbol{K_{\Delta }}\)-Free Graphs

DOI10.1137/21m1440037zbMath1525.05160arXiv2107.00916OpenAlexW4387779320MaRDI QIDQ6081802

Xing Peng, Xiaolan Hu

Publication date: 26 October 2023

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.00916

zbMATH Keywords

fractional chromatic numbercoloringfractional coloring

Mathematics Subject Classification ID

Coloring of graphs and hypergraphs (05C15) Fractional graph theory, fuzzy graph theory (05C72)

Cites Work

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• On an upper bound of the graph's chromatic number, depending on the graph's degree and density
• A strengthening of Brooks' theorem
• The fractional chromatic number of triangle-free graphs with \(\varDelta \leq 3\)
• Edge density and independence ratio in triangle-free graphs with maximum degree three
• The fractional chromatic number of triangle-free subcubic graphs
• Bounding the Fractional Chromatic Number of $K_\Delta$-Free Graphs
• A Fractional Analogue of Brooks' Theorem
• An Upper Bound on the Fractional Chromatic Number of Triangle-Free Subcubic Graphs
• The Fractional Chromatic Number of Graphs of Maximum Degree at Most Three
• Fractional colorings of cubic graphs with large girth
• Some Ramsey-Type Numbers and the Independence Ratio
• Subcubic triangle-free graphs have fractional chromatic number at most 14/5
• A new proof of the independence ratio of triangle-free cubic graphs
• Graph colouring and the probabilistic method

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