Every 4-Connected Graph with Crossing Number 2 is Hamiltonian
نویسندگان
چکیده
منابع مشابه
Every 4-connected line graph of a quasi claw-free graph is hamiltonian connected
Let G be a graph. For any two distinct vertices x and y in G, denote distG(x, y) the distance in G from x and y. For u, v ∈ V (G) with distG(u, v) = 2, denote JG(u, v) = {w ∈ NG(u)∩NG(v)|N(w) ⊆ N [u]∪ N [v]}. A graph G is claw-free if it contains no induced subgraph isomorphic to K1,3. A graph G is called quasi-claw-free if JG(u, v) 6= ∅ for any u, v ∈ V (G) with distG(u, v) = 2. Kriesell’s res...
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 3-connected claw-free Z8-free graph is Hamiltonian
In this article, we first show that every 3-edge-connected graph with circumference at most 8 is supereulerian, which is then applied to show that a 3-connected claw-free graph without Z8 as an induced subgraph is Hamiltonian, where Z8 denotes the graph derived from identifying one end vertex of P9 (a path with 9 vertices) with one vertex of a triangle. The above two results are both best possi...
متن کاملEvery 5-connected planar triangulation is 4-ordered Hamiltonian
A graph G is said to be 4-ordered if for any ordered set of four distinct vertices of G, there exists a cycle in G that contains all of the four vertices in the designated order. Furthermore, if we can find such a cycle as a Hamiltonian cycle, G is said to be 4-ordered Hamiltonian. It was shown that every 4-connected planar triangulation is (i) Hamiltonian (by Whitney) and (ii) 4-ordered (by Go...
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: SIAM Journal on Discrete Mathematics
سال: 2018
ISSN: 0895-4801,1095-7146
DOI: 10.1137/17m1138443