Ke Kang

A Proof of the Tratnik-Ye Medianity Conjecture of Resonance Graphs on Surfaces

We prove the Tratnik--Ye conjecture that every connected component of a resonance graph of perfect matchings on a closed surface is median whenever the allowed even faces form a proper subset of all faces. The embedding need not be cellular or strong, and the graph need not be bipartite. We also show that the quotient...