Subgraphs intersecting any hamiltonian cycle
نویسندگان
چکیده
منابع مشابه
Forbidden subgraphs and Hamiltonian properties of graphs
We consider only finite undirected graphs without loops or multiple edges. Notation or terms not defined here can be found in [1]. Let G be a graph and let S £; V( G). The subgraph (S) induced by S is the graph with vertex set Sand Whose edge set consists of those edges of G incident with two vertices of S. The distance d(u, v) between vertices u and v in a connected graph G is the minimum numb...
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We consider the pair of graphs S and T such that every 3-connected {S, T}-free graph is hamiltonian connected. Such pairs are called hamiltonian connected pairs. We show three new hamiltonian connected pairs. Combing our results and a result of Shepherd, we conclude that if {S, T} is a pair of graphs such that every 2-connected {S, T}-free graph is hamiltonian then every 3-connected {S, T}-free...
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It is proven that if G is a 3-connected claw-free graph which is also Z3-free (where Z3 is a triangle with a path of length 3 attached), P6-free (where P6 is a path with 6 vertices) or H1-free (where H1 consists of two disjoint triangles connected by an edge), then G is hamiltonian-connected. Also, examples will be described that determine a finite family of graphs L such that if a 3-connected ...
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A graph G on n vertices is pancyclic if G contains cycles of all lengths`for 3 ` n and G is cycle extendable if for every nonhamiltonian cycle C G there is a cycle C 0 G such that V (C) V (C 0) and jV (C 0) n V (C)j = 1. We prove that (i) every 2-connected K 1;3-free graph is pancyclic, if G is P 5-free and n 6, if G is P 6-free and n 10, or if G is P 7-free, deer-free and n 14, and (ii) every ...
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Let G = (V, E) be a bipartite graph embedded in a plane (or n-holed torus). Two subgraphs of G differ by a Z-transformation if their symmetric difference consists of the boundary edges of a single face—and if each subgraph contains an alternating set of the edges of that face. For a given φ : V 7→ Z, Sφ is the set of subgraphs of G in which each v ∈ V has degree φ(v). Two elements of Sφ are sai...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1988
ISSN: 0095-8956
DOI: 10.1016/0095-8956(88)90097-4