Combinatorial core of the K₃,₃,₁-redundancy theorem for tetrahedral balls
Alexa's three-dimensional Tutte embedding theorem (Discrete & Computational Geometry, 2025) requires the graph of a tetrahedral mesh to have neither a K₆ nor a K₃,₃,₁ minor and asks whether the second exclusion is necessary. The paper proves that it is redundant for finite simplicial complexes whose realization is a closed topological 3-ball and which satisfy the boundary-triangle condition (BT): if the 1-skeleton G has no K₆ minor, then G is linklessly embeddable and hence has no K₃,₃,₁ minor (Theorem 1.1). This Lean development proves the paper's new combinatorial mathematics over mathlib…
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