Year: 2026
Type: preprint
Abstract: 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 associated with each face is a tree and that these quotients give an isometric embedding of each component into a Cartesian product of trees. This yields a criterion for the facial parity embedding into a hypercube to be isometric.
Source: arXiv (Cornell University)
Authors: Wang, Guangfu, Kang, Ke
Institution: Yantai University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G5189228380
OpenAlex ID: W7212961259