A Fan-type heavy triple of subgraphs for pancyclicity of 2-connected graphs

作者：Widel Wojciech^*

来源：Discrete Mathematics, 2017, 340(7): 1639-1644.

DOI：10.1016/j.disc.2017.03.010

• Fan-type heavy subgraph
• Hamilton cycle
• Pancyclicity

Graph G of order n is said to be pancyclic if it contains cycles of all lengths k for k is an element of {3,... , n}. A vertex v is an element of V(G) is called super-heavy if its degree in G is at least (n+ 1)/2. For a given graph S we say that G is S-f(1)-heavy if for every induced subgraph K of G isomorphic to S and every two vertices u, v is an element of V(K), d(K)(u, v) = 2 implies that at least one of them is super-heavy. For a family of graphs s we say that G is S-f(1)-heavy, if G is S-f(1)-heavy for every graph S is an element of S.
Let H denote the hourglass, a graph consisting of two triangles that have exactly one vertex in common. In this paper we prove that every 2-connected {K-1,(3,) P-7, H}-f(1)-heavy graph on at least nine vertices is pancyclic or missing only one cycle. This result extends the previous work by Faudree, Ryjacek and Schiermeyer.

• 出版日期2017-7