2025/12/10 by Mahabba El Sahili, Sahili, Mahabba El, Ayman El Zein +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Limits and Structures in Graph Theory #Advanced Topology and Set Theory
paper · pdf · doi:10.48550/arxiv.2512.09332
Havet and Thomassé proved that every tournament of order n≥ 8 contains every oriented Hamiltonian path, which was conjectured by Rosenfeld. Recently, it was shown that in any tournament T of order n≥ 8, there exists an arc e such that T-e contains any oriented Hamiltonian path. A natural extension of this problem is to study the stability of this property under arbitrary arc deletion. In this paper, we prove that every arc e in a tournament T of order n≥ 8 satisfies that T-e contains every oriented Hamiltonian path, except for some explicitly described exceptions.