05300608

j

05300608 Korzhik, Vladimir P. Kwak, Jin Ho Nonorientable triangular embeddings of complete graphs with arbitrarily large looseness. Discrete Math. 308, No. 15, 3208-3212 (2008). 2008 Elsevier Science B.V. (North-Holland), Amsterdam EN topological embedding triangular embedding complete graph looseness Steiner triple system

doi:10.1016/j.disc.2007.06.023

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 $p\ge 3$, there is a nonorientable imbedding of a complete graph with looseness at least $p$. Arthur T. White (Kalamazoo)