A note on the number of non-serparating induced cycles in 3-connected graphs
Hanbaek Lyu · arXiv (Cornell University) · 2012
Let $G$ be a simple 3-connected graph. Let $C(G)$ be the set of all induced nonseparating cycles in $G$ and $h(G)$ be the Hadwiger number of $G$. It is shown that $\binom{h(G)}{3} - \binom{h(G)}{2}+\binom{h(G)}{1} \le |C(G)|-|E(G)|+|V(G)|$. This will give a new lower bound of the number of induced nonseparating cyles in 3-connected graphs with large Hadwiger number.