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A Hamilton ℓ -cycle in a k -uniform hypergraph of n -vertex is an ordering of all vertices, combined with an ordered subset C of edges, such that any two consecutive edges share exactly ℓ vertices and each edge in C contains k consecutive vertices. A classic result of O. Ore in 1960 is that if the degree sum of any two independent vertices in an n -vertex graph is at least n , then the...
We call a graph G pancyclic if it contains at least one cycle of every possible length m , for 3 ≤ m ≤ | V ( G ) | . In this paper, we define a new property called chorded pancyclicity. We explore forbidden subgraphs in claw-free graphs sufficient to imply that the graph contains at least one chorded cycle of every possible length 4 , 5 , … , | V ( G ) | . In particular, certain paths...
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