Cream, Megan; Gould, Ronald J.; Larsen, Victor Forbidden subgraphs for chorded pancyclicity. (English) Zbl 1370.05109 Discrete Math. 340, No. 12, 2878-2888 (2017). Summary: We call a graph \(G\) pancyclic if it contains at least one cycle of every possible length \(m\), for \(3 \leq m \leq | V(G) |\). 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 \(4, 5, \ldots, | V(G) |\). In particular, certain paths and triangles with pendant paths are forbidden. MSC: 05C38 Paths and cycles Keywords:pancyclic; chorded cycle; forbidden subgraph; Hamiltonian PDF BibTeX XML Cite \textit{M. Cream} et al., Discrete Math. 340, No. 12, 2878--2888 (2017; Zbl 1370.05109) Full Text: DOI References: [1] Faudree, R. J.; Gould, R. J., Characterizing forbidden pairs for Hamiltonian properties, Discrete Math., 173, 45-60, (1997) · Zbl 0879.05050 [2] Faudree, R. J.; Ryjacek, Z.; Schiermeyer, I., Forbidden subgraphs and cycle extendability, J. Combin. Math. Combin. Comput., 19, 109-128, (1995) · Zbl 0839.05059 [3] Goodman, S.; Hedetniemi, S., Sufficient conditions for a graph to be Hamiltonian, J. Combin. Theory Ser. B, 16, 175-180, (1974) · Zbl 0275.05126 [4] Gould, R. J., Graph Theory, (2012), Dover Pub. Inc Mineola, N.Y. [5] Gould, R. J.; Jacobson, M. S., Forbidden subgraphs and Hamiltonian properties of graphs, Discrete Math., 42, 189-196, (1982) · Zbl 0495.05039 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.