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arXiv · 2608.19024

On the odd independence number of the Queen graph

Martin Knor·Jelena Sedlar·Riste Škrekovski
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Abstract

A set S of vertices of a graph is odd independent if it is independent and every vertex outside S has either zero or an odd number of neighbors in S. The largest size of such a set is the odd independence number alpha_od. Caro, Petrusevski, Skrekovski and Tuza [2] conjectured that alpha_od = 1 for every finite Queen graph. They also asked whether the infinite Queen graph has alpha_od = 1 or alpha_od = infinity. We prove that alpha_od = 1 in both cases. In particular, in the case of an infinite board we prove that alpha_od = 1 holds on the quarter plane and on the whole plane.

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Martin Knor, Jelena Sedlar, Riste Škrekovski. 2026-08-19. On the odd independence number of the Queen graph. https://arxiv.org/abs/2608.19024

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