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- W2982158453 abstract "An oriented path is said to be antisymmetric if listing its arcs in reverse order results in a list where all arcs are reversed. We prove that the number of antisymmetric Hamiltonian paths of a given type is odd in any tournament. As a result, we prove Grünbaum’s conjecture for tournaments of even order; that is, the number of distinct antidirected Hamiltonian paths in a tournament of even order is congruent to 2 (mod4). We also give some precise equalities on the parity of the number of Hamiltonian paths with exactly k backward arcs in a tournament." @default.
- W2982158453 created "2019-11-01" @default.
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- W2982158453 date "2020-04-01" @default.
- W2982158453 modified "2023-09-25" @default.
- W2982158453 title "Parity of paths in tournaments" @default.
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- W2982158453 doi "https://doi.org/10.1016/j.disc.2019.111695" @default.
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