On the circumference of 3-connected cubic triangle-free plane graphs (Q2666403)

Summary: The circumference of a graph \(G\) is the length of a longest cycle in \(G\), denoted by \(\mathrm{cir}(G)\). For any even number \(n\), let \[ c(n) = \min\{\mathrm{cir}(G)\mid G \text{ is a 3-connected cubic triangle-free plane graph with } n \text{ vertices}\}. \] In this paper, we show that an upper bound of \(c(n)\) is \(n+1-3\lfloor n/136\rfloor\) for \(n\geq136\).