N. Hoang, Q. Hoang, M. Rosenfeld

One-factorizations of the complete graph $\mathbb{K}_{2n}$ is a challenging, attractive topic in combinatorics and operations research. In this talk, we introduce a new one-factorization: starter one-factorizations, one-factorizations where every one-factor is a starter. We show that instances can be solved by graph coloring, finding maximum independent sets in graphs, set covering, counting, and binary ILP. As a collateral benefit, we identify many new HBTD(n)s (rainbow-colored hamiltonian balanced tournament designs) and provide evidence that most likely they exist for almost all sizes.

Keywords: starter, factorization, round-robin tournaments


TC2 Integer Optimization
June 10, 2021  12:30 PM
2 - LV Kantorovich

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