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Approximating TSP walks in subcubic graphs.
- Source :
-
Journal of Combinatorial Theory - Series B . Jan2023:Part 2, Vol. 158, p70-104. 35p. - Publication Year :
- 2023
-
Abstract
- We prove that every simple 2-connected subcubic graph on n vertices with n 2 vertices of degree 2 has a TSP walk of length at most 5 n + n 2 4 − 1 , 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 5 n + n 2 4 − 1 and 5 n 4 − 2 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 5 4 -approximation algorithm for the graphic TSP on simple cubic graphs, improving on the previously best known approximation ratio of 9 7. [ABSTRACT FROM AUTHOR]
- Subjects :
- *APPROXIMATION algorithms
*COMBINATORIAL optimization
Subjects
Details
- Language :
- English
- ISSN :
- 00958956
- Volume :
- 158
- Database :
- Academic Search Index
- Journal :
- Journal of Combinatorial Theory - Series B
- Publication Type :
- Academic Journal
- Accession number :
- 160368783
- Full Text :
- https://doi.org/10.1016/j.jctb.2022.09.002