Some properties of the skeleton of the pyramidal tours polytope

doi:10.1016/j.endm.2017.06.030

Electronic Notes in Discrete Mathematics

Volume 61, August 2017, Pages 131-137

https://doi.org/10.1016/j.endm.2017.06.030 Get rights and content

Abstract

We consider the skeleton of the pyramidal tours polytope PYR(n) that is defined as the convex hull of characteristic vectors of all pyramidal tours in the complete graph $K_{n}$ . We describe necessary and sufficient condition for the adjacency of vertices of PYR(n) polytope. Based on that, we establish that the diameter of PYR(n) skeleton equals 2, and the asymptotically exact estimate of PYR(n) skeleton's clique number is $Θ (n^{2})$ . This value characterizes the time complexity in a broad class of algorithms based on linear comparisons.

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¹: The research is supported by the initiative R&D VIP-004 YSU.

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Some properties of the skeleton of the pyramidal tours polytope

Abstract

Oper. Res. Lett.

Nonpolynomial lower bounds for the complexity of the traveling salesman problem in a class of algorithms

Autom. Remote Control

On Graphs of the Cone Decompositions for the Min-Cut and Max-Cut Problems

Int. J. Math. Sci.

Well-Solvable Special Cases of the Traveling Salesman Problem: A Survey

SIAM Rev.