Every 3‐connected, locally connected, claw‐free graph is Hamilton‐connected
نویسندگان
چکیده
منابع مشابه
Every 3-connected, locally connected, claw-free graph is Hamilton-connected
A graph G is locally connected if the subgraph induced by the neighbourhood of each vertex is connected. We prove that a locally connected graph G of order p 3, containing no induced subgraph isomorphic to K 1;3 , is Hamilton-connected if and only if G is 3-connected.
متن کاملEvery N2-Locally Connected claw-Free Graph with Minimum Degree at Least 7 is Z3-Connected
Let G be a 2-edge-connected undirected graph, A be an (additive) abelian group and A∗ = A−{0}. A graph G is A-connected if G has an orientation D(G) such that for every function b : V (G) 7→ A satisfying ∑ v∈V (G) b(v) = 0, there is a function f : E(G) 7→ A ∗ such that for each vertex v ∈ V (G), the total amount of f values on the edges directed out from v minus the total amount of f values on ...
متن کاملEvery 3-connected, essentially 11-connected line graph is Hamiltonian
Thomassen conjectured that every 4-connected line graph is Hamiltonian. A vertex cut X of G is essential if G−X has at least two non-trivial components. We prove that every 3-connected, essentially 11-connected line graph is Hamiltonian. Using Ryjác̆ek’s line graph closure, it follows that every 3-connected, essentially 11-connected claw-free graph is Hamiltonian. © 2005 Elsevier Inc. All rights...
متن کاملEvery Monotone Open 2-homogeneous Metric Continuum Is Locally Connected
In [16, Theorem 3.12, p. 397], Ungar answered a question of Burgess [2] by showing that every 2-homogeneous metric continuum is locally connected. A short, elementary and elegant proof of this result has been given by Whittington [17] who has omitted a powerful result of Effros (viz. Theorem 2.1 of [4, p. 39]) used by Ungar. It is observed in this note that Whittington's proof can be applied to...
متن کاملEvery line graph of a 4-edge-connected graph is I-connected
We prove that every line graph of a 4-edge-connected graph is Z3-connected. In particular, every line graph of a 4-edge-connected graph has a nowhere zero 3-flow.
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 Graph Theory
سال: 1996
ISSN: 0364-9024,1097-0118
DOI: 10.1002/(sici)1097-0118(199610)23:2<191::aid-jgt10>3.3.co;2-2