2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167182We give a criterion which determines when a union of one-dimensional Deligne-Lusztig varieties has a connected closure. We also obtain a new, short proof of the connectedness criterion for Deligne-Lusztig varieties due to Lusztig.v2: Revised Section 3, added Section 4. 6 pagesAlgebraic Geometry14L35; 20G40text