The average solution of a TSP instance in a graph
Stijn Cambie

TL;DR
This paper introduces the concept of average k-TSP distance in graphs, relating it to Steiner distances, and provides bounds and characterizations for these averages based on graph order.
Contribution
It defines the average k-TSP distance, explores its relation to Steiner distances, and establishes bounds and equality conditions for various graph sizes.
Findings
Relation between average k-TSP and Steiner distances
Characterization of equality cases in bounds
Sharp bounds for average k-TSP based on graph order
Abstract
We define the average -TSP distance of a graph as the average length of a shortest walk visiting vertices, i.e. the expected length of the solution for a random TSP instance with uniformly random chosen vertices. We prove relations with the average -Steiner distance and characterize the cases where equality occurs. We also give sharp bounds for given the order of the graph.
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Taxonomy
TopicsAdvanced Graph Theory Research · Stochastic processes and statistical mechanics · Graph theory and applications
