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.
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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: Journal of Graph Theory
سال: 1996
ISSN: 0364-9024,1097-0118
DOI: 10.1002/(sici)1097-0118(199610)23:2<191::aid-jgt10>3.0.co;2-k