A theoretical analysis of backtracking in the graph coloring problem
Journal of Algorithms
Many hard examples for resolution
Journal of the ACM (JACM)
Experimental results on the crossover point in random 3-SAT
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
Using the Groebner basis algorithm to find proofs of unsatisfiability
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A Spectral Technique for Coloring Random 3-Colorable Graphs
SIAM Journal on Computing
A sharp threshold for k-colorability
Random Structures & Algorithms
A machine program for theorem-proving
Communications of the ACM
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
Frozen development in graph coloring
Theoretical Computer Science - Phase transitions in combinatorial problems
Almost all graphs with average degree 4 are 3-colorable
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, Workshop, October 11-13, 1993
The Efficiency of Resolution and Davis--Putnam Procedures
SIAM Journal on Computing
A deterministic (2 - 2/(k+ 1))n algorithm for k-SAT based on local search
Theoretical Computer Science
3-coloring in time 0(1.3446^n): a no-MIS algorithm
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
The analysis of a list-coloring algorithm on a random graph
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Simplified and improved resolution lower bounds
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
The resolution complexity of constraint satisfaction
The resolution complexity of constraint satisfaction
The two possible values of the chromatic number of a random graph
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
A generating function method for the average-case analysis of DPLL
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
On the resolution complexity of graph non-isomorphism
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
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We consider the resolution proof complexity of propositional formulas which encode random instances of graph k-colorability. We obtain a tradeoff between the graph density and the resolution proof complexity. For random graphs with linearly many edges we obtain linear-exponential lower bounds on the size of resolution refutations. For random graphs with n vertices and any @e0, we obtain a lower-bound tradeoff between graph density and refutation size that implies subexponential lower bounds of the form 2^n^^^@d for some @d0 for non-k-colorability proofs of graphs with n vertices and O(n^3^/^2^-^1^/^k^-^@e) edges. We obtain sharper lower bounds for Davis-Putnam-DPLL proofs and for proofs in a system considered by McDiarmid. These proof complexity bounds imply that many natural algorithms for k-coloring or k-colorability have essentially the same exponential tradeoff lower bounds on their running times. We also show that very simple algorithms for k-colorability have upper bounds on their running times that are qualitatively similar to the lower bounds as a function of the graph density.