Kalmanson combinatorial conditions
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.
References
- {{citation
| last = Kalmanson | first = Kenneth
| doi = 10.4153/CJM-1975-104-6
| issue = 5
| journal = Canadian Journal of Mathematics
| mr = 0396329
| pages = 1000–1010
| title = Edgeconvex circuits and the traveling salesman problem
| volume = 27
| year = 1975| doi-access = free
}}.
- {{citation
| last1 = Klinz | first1 = Bettina
| last2 = Woeginger | first2 = Gerhard J. | author2-link = Gerhard J. Woeginger
| doi = 10.1023/A:1009881510868
| issue = 1
| journal = Journal of Combinatorial Optimization
| mr = 1702465
| pages = 51–58
| title = The Steiner tree problem in Kalmanson matrices and in circulant matrices
| volume = 3
| year = 1999}}.
- {{citation
| last1 = Deĭneko | first1 = V. G.
| last2 = van der Veen | first2 = J. A.
| last3 = Rudolf | first3 = R.
| last4 = Woeginger | first4 = G. J. | author4-link = Gerhard J. Woeginger
| issue = 4
| journal = RAIRO Recherche Opérationnelle
| mr = 1491043
| pages = 343–362
| title = Three easy special cases of the Euclidean travelling salesman problem
| volume = 31
| year = 1997| url = https://www.rairo-ro.org/articles/ro/pdf/1997/04/ro1997310403431.pdf
}}.
- {{citation
| last = Okamoto | first = Yoshio
| doi = 10.1016/j.dam.2003.08.005
| issue = 3
| journal = Discrete Applied Mathematics
| mr = 2049654
| pages = 349–369
| title = Traveling salesman games with the Monge property
| volume = 138
| year = 2004| doi-access = free
}}.
- {{citation
| last = Çela | first = Eranda
| isbn = 0-7923-4878-8
| location = Dordrecht
| mr = 1490831
| publisher = Kluwer Academic Publishers
| series = Combinatorial Optimization
| title = The Quadratic Assignment Problem: Theory and Algorithms
| volume = 1
| year = 1998}}.
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