منابع مشابه
Unifying Results on Hamiltonian Claw-free Graphs
This work was motivated by many (recent) papers on hamiltonicity of claw-free graphs, i.e. graphs that do not contain K 1;3 as an induced sub-graph. By combining ideas from these papers with some new observations, we unify several of the existing suuciency results, using a new suucient condition consisting of seven subconditions. If each pair of vertices at distance two of a 2-connected claw-fr...
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A graph is uniquely Hamiltonian if it contains exactly one Hamiltonian cycle. In this note, we prove that claw-free graphs with minimum degree at least 3 are not uniquely Hamiltonian. We also show that this is best possible by exhibiting uniquely Hamiltonian claw-free graphs with minimum degree 2 and arbitrary maximum degree. Finally, we show that a construction due to Entringer and Swart can b...
متن کاملHamiltonian N2-locally connected claw-free graphs
A graph G is N2-locally connected if for every vertex v in G, the edges not incident with v but having at least one end adjacent to v in G induce a connected graph. In 1990, Ryjác̆ek conjectured that every 3-connected N2-locally connected claw-free graph is hamiltonian. This conjecture is proved in this note.
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Let A be a ®nite abelian group and G be a digraph. The boundary of a function f : E G 7! A is a function q f : V G 7! A given by q f v Pe leaving v f eÿ P e entering v f e. The graph G is A-connected if for every b : V G 7! A with P v AV G b v 0, there is a function f : E G 7! Aÿ f0g such that q f b. In [J. Combinatorial Theory, Ser. B 56 (1992) 165±182], Jaeger et al showed th...
متن کاملHamiltonian problem on claw-free and almost distance-hereditary graphs
Let G = (V, E) be a connected graph. The distance between two vertices x and y in G, denoted by dG(x, y), is the length of a shortest path between x and y. A graph G is called almost distance-hereditary, if each connected induced subgraph H of G has the property that dH (u, v) ≤ dG(u, v)+ 1 for every pair of vertices u and v in H . We will confirm that every 2-connected, claw-free and almost di...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1993
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90157-o