Graph-theoretic proof demonstrates an odd independence number of one across finite and infinite queen graphs, resolving open combinatorial conjectures.
We prove that every finite rectangular Queen graph Qp,q and the infinite Queen graph Q_∞ 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 Qp,q and give a boundary criterion for Queen graphs on boards with holes.
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Francisco González (2026) studied this question.
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