Queen Graphs Have Odd Independence Number One
Francisco González · Zenodo (CERN European Organization for Nuclear Research) · 2026
We prove that every finite rectangular Queen graph Q_{p,q} and the infinite Queen graph Q_\infty have odd independence number 1, resolving Conjecture 33 and Problem 34 of Caro, Petruševski, Škrekovski and Tuza. We also determine the strong odd chromatic number of Q_{p,q} and give a boundary criterion for Queen graphs on boards with holes.