Kuipers and Veldman conjectured that any 3-connected claw-free graph with order ν and minimum degree is Hamiltonian for ν sufficiently large.

We strengthen this result for CN-free graphs of higher connectivity. For example, we show 3-connected CN-free graphs are both Hamilton connected and pancyclic.

Aug 10, 2013 · Lai, Shao and Zhan (J Graph Theory 48:142–146, 2005) showed that every 3-connected N 2-locally connected claw-free graph is Hamiltonian.

Nov 18, 2005 · If H is a 3-connected claw-free simple graph with ν ⩾ 196, and if δ(H) ⩾. (ν + 5)/10, then either H is Hamiltonian, or δ(H) = (ν + 5)/10 and cl( ...

Lai, Shao and Zhan (J Graph Theory 48:142---146, 2005 ) showed that every 3-connected N 2-locally connected claw-free graph is Hamiltonian.

Oct 22, 2024 · For each i ∈ {1, 2, 3}, let F i = {H | H is a 3-connected claw-free graph such that cl(H) = L(G) where G is a graph obtained from the Petersen ...

It is shown that every 3-connected claw-free graph G such that every locally disconnected vertex lies on some induced cycle of length at least 4 with at ...

May 8, 2012 · In this article, we consider forbidden subgraphs for hamiltonicity of 3-connected claw-free graphs.

Oct 22, 2024 · A graph G is called claw-free if G has no induced subgraph isomorphic to K 1;3 . A graph G is said to be hamiltonian if it has a cycle ...

Using Ryj ek's closure, we prove that any 3-connected claw-free graph of order and minimum degree +3810 is hamiltonian. This improves a theorem of Kuipers ...