Harris's fractional chromatic number conjecture for triangle-free degenerate graphs
Harris's fractional chromatic number conjecture for triangle-free degenerate graphs
Let be a graph, and let be a nonnegative integer such that is -degenerate, meaning that every subgraph of has a vertex of degree at most . Let -free mean containing no copy of the triangle, and let denote the fractional chromatic number of . Harris's conjecture. If is -degenerate and triangle-free, then
The conjecture predicts a logarithmic improvement over the general degeneracy bound for fractional chromatic number; the paper presents results toward it and later states that it has been resolved, so the conjecture itself is no longer open.
Progress summary
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Sources & referencesView supporting material
Primary source
Anders Martinsson, “Triangle-free d-degenerate graphs have small fractional chromatic number”, arXiv:2501.18238 (2025).
Additional references
2 papers in this index state this conjecture (2018–2025). The statement above is taken from the most recent of them; the others are arXiv:1811.11116.
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