Looseness and independence number of triangulations on closed surfaces
Atsuhiro Nakamoto, Seiya Negami, Kyoji Ohba, Yusuke Suzuki · Discussiones Mathematicae Graph Theory · 2016
The looseness of a triangulation G on a closed surface F 2 , denoted by (G), is defined as the minimum number k such that for any surjection c : V (G) {1, 2, . . . , k + 3}, there is a face uvw of G with c(u), c(v) and c(w) all distinct. We shall bound (G) for triangulations G on closed surfaces by the independence number of G denoted by (G). In particular, for a triangulation G on the sphere, we have