Every 4-connected line graph of a quasi claw-free graph is hamiltonian connected
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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...
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متن کاملEvery 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 line graph of a 4 - edge - connected graph is Z 3 - connected
In [Discrete Math. 230 (2001), 133-141], it is shown that Tutte’s 3-flow conjecture that every 4-edge-connected graph has a nowhere zero 3-flow is equivalent to that every 4-edge-connected line graph has a nowhere zero 3-flow. We prove that every line graph of a 4-edgeconnected graph is Z3-connected. In particular, every line graph of a 4-edge-connected graph has a nowhere zero 3-flow.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.09.045