Rectangles Inscribed in Locally Connected Plane Continua - Morales-Fuentes, Ulises; Villanueva-Segovia, Cristina (Topology Proceedings, 2020)
A plane continuum X is said to admit an inscribed rectangle if for every embedding γ X → R^2, all vertices of at least one Euclidean rectangle lie on γ(X). In this paper, we prove that if a plane continuum X contains a copy of the capital letter H continuum, the simple 4-od, or S^1, then X admits an inscribed rectangle. Also, we prove that the only locally connected plane continua that do not admit an inscribed rectangle are the arc and the simple 3-od.