Let $G$ be a graph with chromatic number $χ (G) = 4$ . If $m_{1} < m_{2} < \dots$ are the lengths of the cycles in $G$ then can $min (m_{i + 1} - m_{i})$ be arbitrarily large? Can this happen if the girth of $G$ is large?

unreviewedOpen. Worked here; no verified result yet.

graph theory · disproved · 0 attempts

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