Stiebitz, Subgraphs of colour-critical graphs, Combinatorica 7 (1987), 303–312

· 1987

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math.CO · 2019-06-23 · unverdicted · novelty 7.0

Any 4-critical graph on n vertices contains Ω(n²) odd cycles, with an improved general bound of Ω(n^{1/(k-2)}) for k≥5.

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Counting critical subgraphs in $k$-critical graphs math.CO · 2019-06-23 · unverdicted · none · ref 10
Any 4-critical graph on n vertices contains Ω(n²) odd cycles, with an improved general bound of Ω(n^{1/(k-2)}) for k≥5.