Geodesic
Edge looseness of plane graphs
Ars Mathematica Contemporanea, Tome 9 (2015) no. 2, pp. 279-286.

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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.
DOI : 10.26493/1855-3974.609.e4d
Keywords: Plane graph, edge coloring. 
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Július Czap. Edge looseness of plane graphs. Ars Mathematica Contemporanea, Tome 9 (2015) no. 2, pp. 279-286. doi : 10.26493/1855-3974.609.e4d. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.609.e4d/

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