Circumference of 3-connected claw-free graphs and large Eulerian subgraphs of 3-edge-connected 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 ...
متن کاملForbidden Subgraphs for Hamiltonicity of 3-Connected Claw-Free Graphs
In this paper, we consider forbidden subgraphs for hamiltonicity of 3-connected claw-free graphs. Let Zi be the graph obtaind from a triangle by attaching a path of length i to one of its vertices, and let Q∗ be the graph obtained from the Petersen graph by adding one pendant edge to each vertex. Lai et al. [J. Graph Theory 64 (2010), no. 1, 1-11] conjectured that every 3-connected {K1,3, Z9}-f...
متن کاملBounding the circumference of 3-connected claw-free graphs
The circumference of a graph is the length of its longest cycles. A result of Jackson and Wormald implies that the circumference of a 3-connected claw-free graph is at least 1 2 n150 . In this paper we improve this lower bound to Ω(n3 ), and our proof implies a polynomial time algorithm for finding a cycle of such length. Bondy and Simonovits showed that Θ(n9 ) is an upper bound. Partially supp...
متن کاملSpanning eulerian subgraphs in N -locally connected claw-free graphs
A graph G is Nm-locally connected if for every vertex v in G, the vertices not equal to v and with distance at most m to v induce a connected subgraph in G. We show that both connected N2-locally connected claw-free graph and 3-edge-connected N3-locally connected claw-free graph have connected even [2, 4]-factors, which settle a conjecture by Li in [6].
متن کاملSpanning eulerian subgraphs in N2-locally connected claw-free graphs
A graph G is Nm-locally connected if for every vertex v in G, the vertices not equal to v and with distance at most m to v induce a connected subgraph in G. We show that both connectedN2-locally connected claw-free graph and 3-edge-connected N3-locally connected claw-free graph have connected even [2, 4]-factors, which settle a conjecture by Li in [6].
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2011
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2011.02.009