A sufficient condition for Hamiltonicity in locally finite graphs

A sufficient condition for Hamiltonicity in locally finite graphs

Using topological circles in the Freudenthal compactification of a graph as infinite cycles, we extend to locally finite graphs a result of Oberly and Sumner on the Hamiltonicity of finite graphs. This answers a question of Stein, and gives a sufficient condition for Hamiltonicity in locally finite graphs.

A sufficient local degree condition for Hamiltonicity in locally finite claw-free graphs

Among the well-known sufficient degree conditions for the Hamiltonicity of a finite graph, the condition of Asratian and Khachatrian is the weakest and thus gives the strongest result. Diestel conjectured that it should extend to locally finite infinite graphs G, in that the same condition implies that the Freudenthal compactification of G contains a circle through all its vertices and ends. We...

A clique-covering sufficient condition for hamiltonicity of graphs

Hamiltonicity in Locally Finite Graphs: Two Extensions and a Counterexample

We state a sufficient condition for the square of a locally finite graph to contain a Hamilton circle, extending a result of Harary and Schwenk about finite graphs. We also give an alternative proof of an extension to locally finite graphs of the result of Chartrand and Harary that a finite graph not containing K4 or K2,3 as a minor is Hamiltonian if and only if it is 2-connected. We show furth...

A new sufficient condition for hamiltonian graphs

The study of Hamiltonian graphs began with Dirac’s classic result in 1952. This was followed by that of Ore in 1960. In 1984 Fan generalized both these results with the following result: If G is a 2-connected graph of order n and max{d(u), d(v)}≥n/2 for each pair of vertices u and v with distance d(u, v)=2, then G is Hamiltonian. In 1991 Faudree–Gould–Jacobson–Lesnick proved that if G is a 2-co...