NP is as easy as detecting unique solutions
Theoretical Computer Science
Computing independent sets in graphs with large girth
Discrete Applied Mathematics
Complexity: knots, colourings and counting
Complexity: knots, colourings and counting
On the NP-completeness of the k-colorability problem for triangle-free graphs
Discrete Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Extremal Graph Theory
Colouring graphs when the number of colours is nearly the maximum degree
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Journal of Combinatorial Theory Series B
A novel giant-subgraph phase-transition in sparse random k-partite graphs
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
Path coupling using stopping times and counting independent sets and colorings in hypergraphs
Random Structures & Algorithms
Dichotomy for bounded degree H-colouring
Discrete Applied Mathematics
A novel giant-subgraph phase-transition in sparse random k-partite graphs
Discrete Applied Mathematics
The complexity of changing colourings with bounded maximum degree
Information Processing Letters
On graphs without a C4 or a diamond
Discrete Applied Mathematics
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For any integer k, we prove the existence of a uniquely k-colourable graph of girth at least g on at most k12(g+1) vertices whose maximal degree is at most 5k13. From this we deduce that, unless NP=RP, no polynomial time algorithm for k-Colourability on graphs G of girth g(G)≥log∣G∣/13logk and maximum degree Δ(G)≤6k13 can exist. We also study several related problems.