Maximum Number of Contractible Edges on Longest Cycles of a \(3\)-Connected Graph

Abstract

We show that if \(G\) is a \(3\)-connected graph of order at least \(5\), then there exists a longest cycle \(C\) of \(G\) such that the number of contractible edges of \(G\) which are on \(C\) is greater than or equal to \(\frac{|V(C)| + 9}{8}.\)