Edge looseness of plane graphs
Július Czap · Ars Mathematica Contemporanea · 2015
A face of an edge colored plane graph is called e-loose if the number of colors used on its edges is at least three. The e-looseness of a plane graph G is the minimum positive integer k such that any edge coloring of G with k colors involves an e-loose face. In this paper we determine tight lower and upper bounds for the e-looseness of connected plane graphs. These bounds are expressed by linear polynomials of the number of faces.