Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, May 09, 2023, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Sebastian Haslebacher

Exact Matching: Characterization on Restricted Graph Classes

Given an integer k and a simple graph G with edges colored red or blue, Exact Matching (EM) is the problem of deciding whether G has a perfect matching containing exactly k red edges. While a randomized polynomial-time algorithm for EM has been known since the 1980s, the best deterministic algorithm to date takes exponential time. However, better deterministic algorithms are known for several restricted graph classes. We extend this line of work with a new characterization of the exact matchings in unit-interval graphs, chain graphs, and complete r-partite graphs. This characterization implies deterministic polynomial-time algorithms on these graph classes. These results are from my master's thesis supervised by Bernd Gärtner and Nicolas El Maalouly.

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