منابع مشابه
Hamiltonicity in Partly claw-free graphs
Matthews and Sumner have proved in [10] that if G is a 2-connected claw-free graph of order n such that δ(G) ≥ (n − 2)/3, then G is Hamiltonian. We say that a graph is almost claw-free if for every vertex v of G, 〈N(v)〉 is 2-dominated and the set A of centers of claws of G is an independent set. Broersma et al. [5] have proved that if G is a 2-connected almost claw-free graph of order n such th...
متن کاملHamiltonicity in 3-connected claw-free graphs
Kuipers and Veldman conjectured that any 3-connected claw-free graph with order ν and minimum degree δ ≥ ν+6 10 is Hamiltonian for ν sufficiently large. In this paper, we prove that if H is a 3-connected claw-free graph with sufficiently large order ν, and if δ(H) ≥ ν+5 10 , then either H is hamiltonian, or δ(H) = ν+5 10 and the Ryjác̆ek’s closure cl(H) of H is the line graph of a graph obtained...
متن کاملOn Hamiltonicity of {claw, net}-free graphs
An st-path is a path with the end-vertices s and t. An s-path is a path with an end-vertex s. The results of this paper include necessary and sufficient conditions for a {claw, net}-free graph G with s, t ∈ V (G) and e ∈ E(G) to have (1) a Hamiltonian s-path, (2) a Hamiltonian st-path, (3) a Hamiltonian sand st-paths containing e when G has connectivity one, and (4) a Hamiltonian cycle containi...
متن کاملNeighborhood intersections and Hamiltonicity in almost claw-free graphs
Abstract: Let G be a graph. The partially squared graph G∗ of G is a graph obtained from G by adding edges uv satisfying the conditions uv 6∈ E(G), and there is some w ∈ N(u) ∩ N(v), such that N(w) ⊆ N(u) ∪ N(v) ∪ {u, v}. Let t > 1 be an integer and Y ⊆ V (G), denote n(Y ) = |{v ∈ V (G) | min y∈Y {distG(v, y)} ≤ 2}|, It(G) = {Z |Z is an independent set of G, |Z| = t}. In this paper, we show tha...
متن کاملToughness and hamiltonicity in almost claw-free graphs
Some known results on claw-free (K 1;3-free) graphs are generalized to the larger class of almost claw-free graphs which were introduced by Ryjj a cek. In particular, we show that a 2-connected almost claw-free graph is 1-tough, and that a 2-connected almost claw-free graph on n vertices is hamiltonian if 1 3 (n ? 2), thereby (partly) generalizing results of Matthews and Sumner. Finally, we use...
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ژورنال
عنوان ژورنال: RAIRO - Operations Research
سال: 2009
ISSN: 0399-0559,1290-3868
DOI: 10.1051/ro/2009007