\((2 \mod 4)\)-Cycles

For two integers \(k > 0\) and \(s (\geq 0\)), a cycle of length \(s\) is called an \((s \mod k)\)-cycle if \(l \equiv s \mod k\). In this paper, the following conjecture of Chen, Dean, and Shreve [5] is proved:Every \(2\)-connected graph with at least six vertices and minimum degree at least three contains a (\(2 \mod 4\))-cycle.