The cycle space of a 3-connected hamiltonian graph
نویسندگان
چکیده
منابع مشابه
On the Cycle Space of a 3–Connected Graph
We give a simple proof of Tutte’s theorem stating that the cycle space of a 3–connected graph is generated by the set of non-separating circuits of the graph.
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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...
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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...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2000
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(99)00396-9