A note on constructive lower bounds for the ramsey numbers R(3, t)
Journal of Combinatorial Theory Series B
Five-coloring graphs on the torus
Journal of Combinatorial Theory Series B
The Ramsey number R(3, t) has order of magnitude t2/log t
Random Structures & Algorithms
Handbook of combinatorics (vol. 2)
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Color-critical graphs on a fixed surface
Journal of Combinatorial Theory Series B - Special issue: dedicated to Professor W. T. Tutte on the occasion of his eightieth birthday
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Topological minors in graphs of large girth
Journal of Combinatorial Theory Series B
Graph Theory With Applications
Graph Theory With Applications
Reducing Hajós' 4-coloring conjecture to 4-connected graphs
Journal of Combinatorial Theory Series B
Hadwiger's conjecture for powers of cycles and their complements
European Journal of Combinatorics
Hajós' conjecture and cycle power graphs
European Journal of Combinatorics
On topological relaxations of chromatic conjectures
European Journal of Combinatorics
List-coloring graphs without subdivisions and without immersions
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Five-coloring graphs on the Klein bottle
Journal of Combinatorial Theory Series B
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Hajós' conjecture is false for almost all graphs but only few explicit counterexamples have appeared in the literature. We relate Hajós' conjecture to Ramsey theory, perfect graphs, and the maximum cut problem and obtain thereby new classes of explicit counterexamples. On the other hand, we show that some of the graphs which Catlin conjectured to be counterexamples to Hajós' conjecture satisfy the conjecture, and we characterize completely the graphs which satisfy Catlin's conjecture.