MathDB

Consider the lattice

L

of the contradictions of a simple graph

G

(as sets of vertex pairs) with respect to inclusion. Let

n \geq 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

Problem Statement