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Circumference of 3-connected claw-free graphs and large Eulerian subgraphs of 3-edge-connected graphs
2011
Journal of combinatorial theory. Series B (Print)
The circumference of a graph is the length of its longest cycles. Results of Jackson, and Jackson and Wormald, imply that the circumference of a 3-connected cubic n-vertex graph is Ω(n 0.694 ), and the circumference of a 3-connected claw-free graph is Ω(n 0.121 ). We generalize and improve the first result by showing that every 3-edge-connected graph with m edges has an Eulerian subgraph with Ω(m 0.753 ) edges. We use this result together with the Ryjáček closure operation to improve the lower
doi:10.1016/j.jctb.2011.02.009
fatcat:cvfcg7aaefgo5nxuotyeidbvii