Cycles of consecutive lengths in 3-connected graphs
Abstract
Recently Lin, Wang and Zhou have proved that every 3-connected nonbipartite graph of minimum degree at least k with k 6 and order at least k+2 contains k cycles of consecutive lengths. They also conjecture that this result is true for k=4, 5. We prove this conjecture. Our proofs use many ideas of Gao, Huo, Liu and Ma.
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