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Erdős problem 751

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Let GG be a graph with chromatic number χ(G)=4\chi(G)=4. If m1<m2<⋯m_1<m_2<\cdots are the lengths of the cycles in GG then can min⁡(mi+1−mi)\min(m_{i+1}-m_i) be arbitrarily large? Can this happen if the girth of GG is large?

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Problem row
sha256:13169476f19e5182abee51faa034a7bc7ccd9ab0e0125c7d1bd24977f0711398
Metadata
sha256:83d0480a2609d718d90e632266a011ec7fc6fd371cf300696c9483317ace1fe4
Observation
sha256:9c8326e865b6017b103af7611c852a06776d81964979b8ab5a1b800cd550dff6
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sha256:b8005e6c9935df09ada637c0bc0aac9d179e53483c572483739cd45f93ba3d45
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sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
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sha256:a4a96441668a9f8b33afbcb3f696a2639f5fae145f36ddc063d7f67d5fb87ce8
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36c6d0fef71a3fec84d9dcd5eeca4e22e378f7cb
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