Edge looseness of plane graphs

Július Czap

Abstract


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.


Keywords


Plane graph, edge coloring.

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DOI: https://doi.org/10.26493/1855-3974.609.e4d

ISSN: 1855-3974

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