The Odd Independence Number of the Infinite Queen Graph

August 12, 2026Open Access

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Key Points

Determine the odd independence number of the infinite Queen graph to resolve Problem 34 posed by Caro, Petruševski, Škrekovski, and Tuza.
Combinatorial and graph-theoretic proof techniques applied to infinite grid graphs.
Structural analysis of non-attacking queen placements across infinite chessboard dimensions.
The exact value of the odd independence number for the infinite Queen graph is formally established.
Problem 34 of Caro, Petruševski, Škrekovski, and Tuza is completely resolved.

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Mathematical analysis reveals the exact odd independence number of the infinite Queen graph, resolving an open problem in graph theory.

We determine the odd independence number of the infinite Queen graph, resolving Problem 34 of Caro, Petruševski, Škrekovski and Tuza.

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Francisco González (2026) studied this question.

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