Approximating TSP walks in sub cubic graphs

Series
Graph Theory Seminar
Time
Tuesday, February 15, 2022 - 3:45pm for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Youngho Yoo – Georgia Institute of Technology – yyoo41@gatech.eduhttps://people.math.gatech.edu/~yyoo41/
Organizer
Anton Bernshteyn

We prove that every simple 2-connected subcubic graph on n vertices with n2 vertices of degree 2 has a TSP walk of length at most 5n+n241, confirming a conjecture of Dvořák, Král', and Mohar. This bound is best possible; there are infinitely many subcubic and cubic graphs whose minimum TSP walks have lengths 5n+n241 and 5n42 respectively. We characterize the extremal subcubic examples meeting this bound. We also give a quadratic-time combinatorial algorithm for finding such a TSP walk. In particular, we obtain a 54-approximation algorithm for the graphic TSP on simple cubic graphs, improving on the previously best known approximation ratio of 97.