A SUFFICIENT CONDITION FOR PANCYCLIC GRAPHS

Abstract A graph G is called an $[s,t]$ -graph if any induced subgraph of G of order s has size at least $t.$ We prove that every $2$ -connected $[4,2]$ -graph of order at least $7$ is pancyclic. This strengthens existing results. There are $2$ -connected $[4,2]$ -graphs which do not satisfy the Chvátal–Erdős condition on Hamiltonicity. We also determine the triangle-free graphs among $[p+2,p]$ -graphs for a general $p.$