The Average Solution of a TSP Instance in a Graph

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2025-02-16 DOI:10.1002/jgt.23232

Stijn Cambie

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引用次数: 0

Abstract

We define the average $k$ -TSP distance $μ_{tsp, k}$ of a graph $G$ as the average length of a shortest closed walk visiting $k$ vertices, that is, the expected length of the solution for a random TSP instance with $k$ uniformly random chosen vertices. We prove relations with the average $k$ -Steiner distance and characterize the cases where equality occurs. We also give sharp bounds for $μ_{tsp, k} (G)$ given the order of the graph.

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图中TSP实例的平均解

我们定义k -TSP平均距离μ tsp，取图G的k为经过k个顶点的最短封闭行走的平均长度，即：具有k个一致随机选择顶点的随机TSP实例的解的期望长度。我们用平均k -Steiner距离证明了这种关系，并描述了等式发生的情况。我们也给出了μ tsp的明确界限，k (G)给出图的阶数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .