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2011

Circumference of 3-connected claw-free graphs and large Eulerian subgraphs of 3-edge-connected graphs

9 years 4 months ago
Circumference of 3-connected claw-free graphs and large Eulerian subgraphs of 3-edge-connected graphs
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(n0.694 ), and the circumference of a 3-connected claw-free graph is Ω(n0.121 ). We generalise and improve the first result by showing that every 3-edge-connected graph with m edges has an Eulerian subgraph with Ω(m0.753 ) edges. We use this result together with the Ryj´aˇcek closure operation to improve the lower bound on the circumference of a 3-connected claw-free graph to Ω(n0.753 ). Our proofs imply polynomial time algorithms for finding large Eulerian subgraphs of 3-edge-connected graphs and long cycles in 3-connected claw-free graphs. ∗ School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA. Partially supported by NSF VIGRE Grant † School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, England ‡ School of Mathematics, Georgia I...
Mark Bilinski, Bill Jackson, Jie Ma, Xingxing Yu
Added 01 Jun 2011
Updated 01 Jun 2011
Type Journal
Year 2011
Where JCT
Authors Mark Bilinski, Bill Jackson, Jie Ma, Xingxing Yu
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