On the 2-Vertex Fault Hamiltonicity for Graphs satisfying Ore's Theorem
Hsiu-Chunj Pan,
Hsun Su,
Shin-Shin Kao
Abstract:For any undirected and simple graph G = (V, E), where V denotes the vertex set and E the edge set of G. G is called hamiltonian if it contains a cycle that visits each vertex of G exactly once. Ore (1960) ≥ n holds for every nonadjacent pair of vertices u and v in V , where n is the total number of distinct vertices of G. Kao et al. (2012) proved that any graph G satisfying Ore's theorem remains hamiltonian after the removal of any vertex x ∈ V unless G belongs to one of the two exceptional families of graphs.… Show more
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