The effect of number of Hamiltonian paths on the complexity of a vertex-coloring problem
SIAM Journal on Computing
Combinatorial search
Searching for acyclic orientations of graphs
Discrete Mathematics
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
The acyclic orientation game on random graphs
Random Graphs 93 Proceedings of the sixth international seminar on Random graphs and probabilistic methods in combinatorics and computer science
Gadgets, Approximation, and Linear Programming
SIAM Journal on Computing
Some optimal inapproximability results
Journal of the ACM (JACM)
Sorting 13 Elements Requires 34 Comparisons
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Gadgets Approximation, and Linear Programming
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Constant time parallel sorting: an empirical view
Journal of Computer and System Sciences
New Results in Minimum-Comparison Sorting
Algorithmica
The effect of number of Hamiltonian paths on the complexity of a vertex-coloring problem
SFCS '81 Proceedings of the 22nd Annual Symposium on Foundations of Computer Science
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Let c(G) be the smallest number of edges we have to test in order to determine an unknown acyclic orientation of the given graph G in the worst case. For example, if G is the complete graph on n vertices, then c(G) is the smallest number of comparisons needed to sort n numbers. We prove that c(G) ≤ (1/4 + o(1))n2 for any graph G on n vertices, answering in the affirmative a question of Aigner, Triesch and Tuza [Discrete Mathematics144 (1995) 3–10]. Also, we show that, for every ϵ 0, it is NP-hard to approximate the parameter c(G) within a multiplicative factor 74/73 − ϵ.