TY  - JOUR
ID  - Ivančo2016
LB  - Ivančo2016
AU  - Ivančo, Jaroslav
TI  - M<sub>2</sub>-edge colorings of dense graphs
ST  - M<sub>2</sub>-edge colorings of dense graphs
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2016
VL  - 36
IS  - 5
SP  - 603
EP  - 612
DO  - http://dx.doi.org/10.7494/OpMath.2016.36.5.603
UR  - http://dx.doi.org/10.7494/OpMath.2016.36.5.603
AB  - An edge coloring \(\varphi\) of a graph \(G\) is called an \(\mathrm{M}_i\)-edge coloring if \(|\varphi(v)|\leq i\) for every vertex \(v\) of \(G\), where \(\varphi(v)\) is the set of colors of edges incident with \(v\). Let \(\mathcal{K}_i(G)\) denote the maximum number of colors used in an \(\mathrm{M}_i\)-edge coloring of \(G\). In this paper we establish some bounds of \(\mathcal{K}_2(G)\), present some graphs achieving the bounds and determine exact values of \(\mathcal{K}_2(G)\) for dense graphs.
KW  - edge coloring
KW  - dominating set
KW  - dense graphs
SN  - 1232-9274
ER  -