Every graph with girth 2ℓ (ℓ ≥ 5) and no even hole longer than 2ℓ is 3-colorable.
Chen, Graphs with girth 2 ℓ + 1 and without longer odd holes are 3-colorable, J
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Graphs with girth $2\ell$ and without longer even holes are $3$-colorable
Every graph with girth 2ℓ (ℓ ≥ 5) and no even hole longer than 2ℓ is 3-colorable.