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About this paper
Samuel Fiorini, J. Pascal Gollin, Tony Huynh, Simon Keil, O-joung Kwon, Sang-il Oum, Roohani Sharma, Stefan Weltge
The authors prove polynomial-time solvability, for each fixed Δ, of nine graph-problem families when their specified natural integer-programming formulations have totally Δ-modular coefficient matrices, meaning every square submatrix has determinant magnitude at most Δ. The families include weighted dominating set and traveling salesman. The results use problem-specific graph structure; they do not resolve the general integer-programming question for Δ≥3.
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