Nonorientable triangular embeddings of complete graphs with arbitrarily large looseness (Q932590)

The looseness of a triangular imbedding of a complete graph \(G\) in a closed surface is the minimum integer m such that every assignment of \(m\) colors to the vertices of \(G\) yields a face incident with vertices of three distinct colors. The authors show that for every \(p\geq 3\), there is a nonorientable imbedding of a complete graph with looseness at least \(p\).