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Forbidden subgraphs for chorded pancyclicity. (English) Zbl 1370.05109
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
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