Kalmanson combinatorial conditions

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In mathematics, the Kalmanson combinatorial conditions are a set of conditions on the distance matrix used in determining the solvability of the traveling salesman problem. These conditions apply to a special kind of cost matrix, the Kalmanson matrix, and are named after Kenneth Kalmanson.


  • Kalmanson, Kenneth (1975), "Edgeconvex circuits and the traveling salesman problem", Canadian Journal of Mathematics, 27 (5): 1000–1010, MR 0396329, doi:10.4153/CJM-1975-104-6 .
  • Klinz, Bettina; Woeginger, Gerhard J. (1999), "The Steiner tree problem in Kalmanson matrices and in circulant matrices", Journal of Combinatorial Optimization, 3 (1): 51–58, MR 1702465, doi:10.1023/A:1009881510868 .
  • Deĭneko, V. G.; van der Veen, J. A.; Rudolf, R.; Woeginger, G. J. (1997), "Three easy special cases of the Euclidean travelling salesman problem", RAIRO Recherche Opérationnelle, 31 (4): 343–362, MR 1491043 .
  • Okamoto, Yoshio (2004), "Traveling salesman games with the Monge property", Discrete Applied Mathematics, 138 (3): 349–369, MR 2049654, doi:10.1016/j.dam.2003.08.005 .
  • Çela, Eranda (1998), The Quadratic Assignment Problem: Theory and Algorithms, Combinatorial Optimization, 1, Dordrecht: Kluwer Academic Publishers, ISBN 0-7923-4878-8, MR 1490831 .