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This research aims to explore theorem search methods for balanced independent sets in ladder-derived graph families.

March 31, 2026Open Access

Adjacent-Transfer Theorem Search: A Validated Five-Theorem Cluster for Balanced Independent Sets on Ladder-Derived Graphs

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Case study demonstrates theorem search for balanced independent sets in specific graph families, highlighting proof validation.

This research aims to explore theorem search methods for balanced independent sets in ladder-derived graph families.
Analyzed five types of ladder-derived graphs: ladders, prisms, Mobius ladders, and their diagonal counterparts.
Followed a structured workflow including conjecture compression and validated proof routes.
Generated exact formulas for maximum balanced independent set sizes with fixed parity-class partitions.
Developed a validated cluster of five theorems related to independent sets.
Presented lower-bound constructions and zero-sum constraints for balancedness.
Identified novelty status, with some theorems carrying risks of prior art.

Brian Philippe M. Saturnino (2026) studied this question.

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