Convex subgraphs and spanning trees of the square cycles

Abstract

We classify connected spanning convex subgraphs of the square cycles. We then show that every spanning tree of $C_n^2$ is contained in a unique nontrivial connected spanning convex subgraph of $C_n^2$. As a result, we obtain a purely combinatorial derivation of the formula for the number of spanning trees of the square cycles.

6 pages