On Colouring Partial Joins of a Complete Graph and a Cycle
Michael Stiebitz, W. Wessel · Mathematische Nachrichten · 1993
Abstract Define the partial join of two graphs to be some graph arising from their disjoint union by adding a set of new edges each joining a vertex of the first graph and a vertex of the second one. We characterize all colour‐critical graphs being partial joins of a complete graph and an odd cycle thus completely answering a special case of a question raised by T. GALLAI in 1969.