Czechoslovak Mathematical Journal, first online, pp. 1-21
Forbidden subgraphs for chorded pancyclicity
Tao WANG, Xiaojing YANG
Received July 25, 2024. Published online September 14, 2026.
Abstract: A graph $G$ is called pancyclic if it contains cycles of all lengths from 3 to $|V(G)|$. M. Cream, R. J. Gould, V. Larsen (2017) introduced a new property called chorded pancyclicity: A graph $G$ is called chorded pancyclic if it contains chorded cycles of all lengths from 4 to $|V(G)|$. They provided a characterization of forbidden subgraphs for chorded pancyclicity in 2-connected graphs. We prove that 2-connected $\{K_{1,3},Z_3\}$-free graphs are either chorded pancyclic or some exceptional graphs, thus enhancing a previous result by M. Cream, R. J. Gould, V. Larsen (2017). Additionally, we establish that 3-connected $\{K_{1,3},Z_4\}$-free or $\{K_{1,3},P_7\}$-free graphs are chorded pancyclic or some exceptional graphs with small order, which improves some results for 3-connected pancyclic graphs.
Affiliations: Tao Wang, Center for Applied Mathematics, Henan University, Minglun St., Shunhe Hui District, Kaifeng, 475004, P. R. China, e-mail: wangtao@henu.edu.cn; Xiaojing Yang (corresponding author), School of Mathematics and Statistics, Henan University, Minglun St., Shunhe Hui District, Kaifeng, 475004, P. R. China, e-mail: yangxiaojing@henu.edu.cn
