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This research establishes the concept of bilateral deficiency and its relationship with independent domination in graphs.

August 11, 2026Open Access

Bilateral Deficiency: Residual SAT Optimisation and Independent Domination in Regular-DIM Graphs

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Unrefereed candidate defines bilateral deficiency and explores its implications in regular graphs.

This research establishes the concept of bilateral deficiency and its relationship with independent domination in graphs.
Defines bilateral deficiency as the minimum deficiency of a bipolar residual restriction.
Proves a size-preserving bijection with independent dominating sets of clause-literal formula graphs.
Constructs a 7/6 upper bound within the cubic-DIM class.
Bilateral deficiency is shown to equal the gap i(G) - μ*(G) for regular graphs with a dominating induced matching.
A minimum order of 50 is identified as necessary for violations in cubic graphs with a specific matching.
Various finite checks, including semantic and structural validations, are included in the core artifact.

Anonymous (2026) studied this question.

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