A generalized implicit enumeration algorithm for graph coloring
Communications of the ACM - Lecture notes in computer science Vol. 174
The hardest constraint problems: a double phase transition
Artificial Intelligence
A correction to Brelaz's modification of Brown's coloring algorithm
Communications of the ACM
New methods to color the vertices of a graph
Communications of the ACM
Frozen development in graph coloring
Theoretical Computer Science - Phase transitions in combinatorial problems
Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, Workshop, October 11-13, 1993
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Constraint Propagation in Graph Coloring
Journal of Heuristics
Systematic Generation of Very Hard Cases for Graph 3-Colorability
TAI '95 Proceedings of the Seventh International Conference on Tools with Artificial Intelligence
Constraint Processing
A new look at the easy-hard-easy pattern of combinatorial search difficulty
Journal of Artificial Intelligence Research
Where the really hard problems are
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
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In this paper we propose a constructive algorithm using constraint propagation to generate 4-critical graph units (4-CGUs) which have only one triangle as subgraph. Based on these units we construct 4-critical graphs using Hajós' join construction. By choosing Grotztsch graph as the initial graph and carefully selecting the edge to be joined, we make sure that the generated graphs are 4-critical and triangle-free. Experiments show that these graphs are exceptionally hard for backtracking algorithms adopting Brélaz's heuristics. We also give some preliminary analysis on the source of hardness.