منابع مشابه
Every 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 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 2-choosable graph is circular consecutive 2-choosable
Suppose G is a graph, r is a positive real number and S(r) is a circle of perimeter r. For a positive real number t ≤ r, a (t, r)circular consecutive colour-list assignment L is a mapping that assigns to each vertex v of G an interval L(v) of S(r) of length t. A circular L-colouring of G is a mapping f : V (G) → S(r) such that for each vertex v, f(v) ∈ L(v) and for each edge uv, the distance be...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2000
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(99)00141-9