Long Cycles and 3-Connected Spanning Subgraphs of Bounded Degree in 3-Connected K1, d-Free Graphs
نویسندگان
چکیده
منابع مشابه
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(n), and the circumference of a 3-connected claw-free graph is Ω(n). We generalise and improve the first result by showing that every 3-edge-connected graph with m edges has an Eulerian subgraph with Ω(m) edges. We ...
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Moon and Moser in 1963 conjectured that if G is a 3-connected planar graph on n vertices, then G contains a cycle of length at least Ω(nlog3 2). In this paper, this conjecture is proved. In addition, the same result is proved for 3-connected graphs embeddable in the projective plane, or the torus, or the Klein bottle. MSC Primary 05C38 and 05C50 Secondary 57M15 Partially supported by NSA grant ...
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By Petersen’s theorem, a bridgeless cubic graph has a 2-factor. H. Fleischner extended this result to bridgeless graphs of minimum degree at least three by showing that every such graph has a spanning even subgraph. Our main result is that, under the stronger hypothesis of 3-edge-connectivity, we can find a spanning even subgraph in which every component has at least five vertices. We show that...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1995
ISSN: 0095-8956
DOI: 10.1006/jctb.1995.1013