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Computer Science > Logic in Computer Science

arXiv:1907.00929 (cs)
[Submitted on 1 Jul 2019 (v1), last revised 15 Jul 2019 (this version, v2)]

Title:Trimming Graphs Using Clausal Proof Optimization

Authors:Marijn J.H. Heule
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Abstract:We present a method to gradually compute a smaller and smaller unsatisfiable core of a propositional formula by minimizing proofs of unsatisfiability. The goal is to compute a minimal unsatisfiable core that is relatively small compared to other minimal unsatisfiable cores of the same formula. We try to achieve this goal by postponing deletion of arbitrary clauses from the formula as long as possible---in contrast to existing minimal unsatisfiable core algorithms. We applied this method to reduce the smallest known unit-distance graph with chromatic number 5 from 553 vertices and 2720 edges to 529 vertices and 2670 edges.
Comments: arXiv admin note: text overlap with arXiv:1805.12181
Subjects: Logic in Computer Science (cs.LO); Combinatorics (math.CO)
Cite as: arXiv:1907.00929 [cs.LO]
  (or arXiv:1907.00929v2 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.1907.00929

Submission history

From: Marijn Heule [view email]
[v1] Mon, 1 Jul 2019 17:06:14 UTC (1,186 KB)
[v2] Mon, 15 Jul 2019 13:59:43 UTC (1,186 KB)
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