Abstract
A graph G is said to be pancyclic if G contains cycles of lengths from 3 to |V(G)|. For a positive integer i, we use \(Z_i\) to denote the graph obtained by identifying an endpoint of the path \(P_{i+1}\) with a vertex of a triangle. In this paper, we show that every 4-connected claw-free \(Z_8\)-free graph is either pancyclic or is the line graph of the Petersen graph. This implies that every 4-connected claw-free \(Z_6\)-free graph is pancyclic, and every 5-connected claw-free \(Z_8\)-free graph is pancyclic.
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Lai, HJ., Zhan, M., Zhang, T. et al. Pancyclicity of 4-Connected \(\{K_{1,3},Z_8\}\)-Free Graphs. Graphs and Combinatorics 35, 67–89 (2019). https://doi.org/10.1007/s00373-018-1987-4
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DOI: https://doi.org/10.1007/s00373-018-1987-4