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Youngho Yoo (유영호), Approximating TSP walks in subcubic graphs

Tuesday, January 3, 2023 @ 4:30 PM - 5:30 PM KST

Room B332, IBS (기초과학연구원)

The Graphic Travelling Salesman Problem is the problem of finding a spanning closed walk (a TSP walk) of minimum length in a given connected graph. The special case of the Graphic TSP on subcubic graphs has been studied extensively due to their worst-case behaviour in the famous $\frac{4}{3}$-integrality-gap conjecture on the “subtour elimination” linear programming relaxation of the Metric TSP.

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 $\frac{5n+n_2}{4}-1$, confirming a conjecture of Dvořák, Král’, and Mohar. This bound is best possible and we characterize the extremal subcubic examples meeting this bound. We also give a quadratic time combinatorial algorithm to find such a TSP walk. In particular, we obtain a $\frac{5}{4}$-approximation algorithm for the Graphic TSP on cubic graphs. Joint work with Michael Wigal and Xingxing Yu.


Tuesday, January 3, 2023
4:30 PM - 5:30 PM KST
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Room B332
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Sang-il Oum (엄상일)
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IBS 이산수학그룹 Discrete Mathematics Group
기초과학연구원 수리및계산과학연구단 이산수학그룹
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IBS Discrete Mathematics Group (DIMAG)
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