A clique-covering sufficient condition for hamiltonicity of graphs

A clique-covering sufficient condition for hamiltonicity of 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.

Clique covering and degree conditions for hamiltonicity in claw-free graphs

By using the closure concept introduced by the last author, we prove that for any suuciently large nonhamiltonian claw-free graph G satisfying a degree condition of type k (G) > n + k 2 ? 4k + 7 (where k is a constant), the closure of G can be covered by at most k ? 1 cliques. Using structural properties of the closure concept, we show a method for characterizing all such nonhamiltonian excepti...

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...

Edge Clique Covering Sum of Graphs

The edge clique cover sum number (resp. edge clique partition sum number) of a graph G, denoted by scc(G) (resp. scp(G)), is defined as the smallest integer k for which there exists a collection of complete subgraphs of G, covering (resp. partitioning) all edges of G such that the sum of sizes of the cliques is at most k. By definition, scc(G) 5 scp(G). Also, it is known that for every graph G ...