Consider the lattice L of the contradictions of a simple graph G (as sets of vertex pairs) with respect to inclusion. Let n≥1 be an arbitrary integer. Show that the identity x \bigwedge \left( \bigvee_{i\equal{}0}^n y_i \right) \equal{} \bigvee_{j\equal{}0}^n
\left( x \bigwedge \left( \bigvee_{0 \leq i \leq n, \;i\not\equal{}j\ } y_i \right)\right) holds if and only if G has no cycle of size at least n\plus{}2.
A. Huhn combinatorics proposedcombinatorics