1Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 403-407
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Sebastian Babiński; Andrzej Grzesik; Sebastian Babiński; Andrzej Grzesik. Maximal edge-colorings of graphs. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 403-407. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a7/
@article{AMUC_2019_88_3_a7,
author = {Sebastian Babi\'nski and Andrzej Grzesik and Sebastian Babi\'nski and Andrzej Grzesik},
title = { Maximal edge-colorings of graphs},
journal = {Acta mathematica Universitatis Comenianae},
pages = {403--407},
year = {2019},
volume = {88},
number = {3},
url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a7/}
}
TY - JOUR
AU - Sebastian Babiński
AU - Andrzej Grzesik
AU - Sebastian Babiński
AU - Andrzej Grzesik
TI - Maximal edge-colorings of graphs
JO - Acta mathematica Universitatis Comenianae
PY - 2019
SP - 403
EP - 407
VL - 88
IS - 3
UR - http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a7/
ID - AMUC_2019_88_3_a7
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%0 Journal Article
%A Sebastian Babiński
%A Andrzej Grzesik
%A Sebastian Babiński
%A Andrzej Grzesik
%T Maximal edge-colorings of graphs
%J Acta mathematica Universitatis Comenianae
%D 2019
%P 403-407
%V 88
%N 3
%U http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a7/
%F AMUC_2019_88_3_a7
For graph G of order n a maximal edge-coloring is a proper partial coloring with fixed number of colors (equal to n or n-1) such that adding any edge to G in any color makes it improper. Meszka and Tyniec proved that for some numbers of edges it is impossible to find such a graph, and provided constructions for some other numbers of edges. However, for many values, the problem remained open. We give a complete solution of this problem for all even values of n and for odd n not smaller than 37.
