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A SUFFICIENT CONDITION FOR PANCYCLIC GRAPHS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society , First View
- Published online by Cambridge University Press:
- 20 December 2024, pp. 1-7
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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 
$p.$
