Journal of the ACM (JACM)
Many hard examples for resolution
Journal of the ACM (JACM)
The graph isomorphism problem: its structural complexity
The graph isomorphism problem: its structural complexity
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
A machine program for theorem-proving
Communications of the ACM
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
The Cutting Plane Proof System with Bounded Degree of Falsity
CSL '91 Proceedings of the 5th Workshop on Computer Science Logic
Completeness results for graph isomorphism
Journal of Computer and System Sciences
Simplified and improved resolution lower bounds
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
On the Hardness of Graph Isomorphism
SIAM Journal on Computing
Bounded Color Multiplicity Graph Isomorphism is in the #L Hierarchy
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
The Resolution Complexity of Independent Sets and Vertex Covers in Random Graphs
Computational Complexity
Polynomial-time algorithms for permutation groups
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
The resolution complexity of random graph k-colorability
Discrete Applied Mathematics
An improved satisfiable SAT generator based on random subgraph isomorphism
Canadian AI'11 Proceedings of the 24th Canadian conference on Advances in artificial intelligence
Notes on generating satisfiable SAT instances using random subgraph isomorphism
AI'10 Proceedings of the 23rd Canadian conference on Advances in Artificial Intelligence
Satisfiability, Branch-Width and Tseitin tautologies
Computational Complexity - Special issue in memory of Misha Alekhnovich
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For a pair of given graphs we encode the isomorphism principle in the natural way as a CNF formula of polynomial size in the number of vertices, which is satisfiable if and only if the graphs are isomorphic. Using the CFI graphs from [12], we can transform any undirected graph G into a pair of non-isomorphic graphs. We prove that the resolution width of any refutation of the formula stating that these graphs are isomorphic has a lower bound related to the expansion properties of G. Using this fact, we provide an explicit family of non-isomorphic graph pairs for which any resolution refutation requires an exponential number of clauses in the size of the initial formula. These graphs pairs are colored with color multiplicity bounded by 4. In contrast we show that when the color classes are restricted to have size 3 or less, the non-isomorphism formulas have tree-like resolution refutations of polynomial size.