Mathematical Programming: Series A and B
On the complexity of cooperative solution concepts
Mathematics of Operations Research
A New Class of Pyramidally Solvable Symmetric Traveling Salesman Problems
SIAM Journal on Discrete Mathematics
Perspectives of Monge properties in optimization
Discrete Applied Mathematics
On the complexity of testing membership in the core of min-cost spanning tree games
International Journal of Game Theory
Sometimes Travelling is Easy: The Master Tour Problem
SIAM Journal on Discrete Mathematics
Pyramidal tours with step-backs and the asymmetric traveling salesman problem
Discrete Applied Mathematics
Gilmore-gomory type traveling salesman problems
Computers and Operations Research - Special issue on the traveling salesman problem
Pyramidal traveling salesman problem
Computers and Operations Research - Special issue on the traveling salesman problem
Cooperative facility location games
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Naturally submodular digraphs and forbidden digraph configurations
Discrete Applied Mathematics
Algorithmic Aspects of the Core of Combinatorial Optimization Games
Mathematics of Operations Research
A combinatorial algorithm minimizing submodular functions in strongly polynomial time
Journal of Combinatorial Theory Series B
An asymmetric analogue of van der Veen conditions and the traveling salesman problem
Discrete Applied Mathematics
A combinatorial strongly polynomial algorithm for minimizing submodular functions
Journal of the ACM (JACM)
On the computation of the nucleolus of a cooperative game
International Journal of Game Theory
Discrete Applied Mathematics
A fully combinatorial algorithm for submodular function minimization
Journal of Combinatorial Theory Series B
The Structure of Circular Decomposable Metrics
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Total balancedness condition for Steiner tree games
Discrete Applied Mathematics
Four point conditions and exponential neighborhoods for symmetric TSP
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On the complexity of core, kernel, and bargaining set
Artificial Intelligence
Approximate fair cost allocation in metric traveling salesman games
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
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Several works have indicated the relationships between polynomially solvable combinatorial optimization problems and the core non-emptiness of cooperative games associated with them, and between intractable combinatorial optimization problems and the hardness of the problem to decide the core non-emptiness of the associated games. In this paper, we study the core of a traveling salesman game, which is associated with the traveling salesman problem. First, we show that in general the problem to test the core non-emptiness of a given traveling salesman game is NP-hard. This corresponds to the NP-hardness of the traveling salesman problem. Second, we show that the core of a traveling salesman game is non-empty if the distance matrix is a symmetric Monge matrix, and also that a traveling salesman game is submodular (or concave) if the distance matrix is a Kalmanson matrix. These correspond to the fact that the Monge property and the Kalmanson property are polynomially solvable special cases of the traveling salesman problem.