Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

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

Mittagsseminar Talk Information

Date and Time: Thursday, November 18, 2021, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Nicolas El Maalouly

Exact Matching in Graphs with Small Independence Number

In the Exact Matching problem, we are given a graph with edges colored red and blue, and an integer k. The goal is to output a perfect matching with exactly k red edges. After introducing the problem in 1982, Papadimitriou and Yannakakis conjectured it to be NP-hard. Soon after, however, Mulmuley et al. proved that it can be solved in randomized polynomial time, which makes it unlikely to be NP-hard. Determining whether Exact Matching is in P remains an open problem and very little progress has been made towards that goal. For special graph classes Yuster showed that Exact Matching is in P for K_3,3-minor free graphs, which include planar graphs. Karzanov showed that it is in P for complete and bipartite complete graphs. In this talk I will show how to solve Exact Matching on graphs of bounded independence number. This is joint work with Raphael Steiner.

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