TY  - JOUR
ID  - Eschouf2015
LB  - Eschouf2015
AU  - Eschouf, Noureddine Ikhlef
AU  - Blidia, Mostafa
TI  - On b-vertex and b-edge critical graphs
ST  - On b-vertex and b-edge critical graphs
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2015
VL  - 35
IS  - 2
SP  - 171
EP  - 180
DO  - http://dx.doi.org/10.7494/OpMath.2015.35.2.171
UR  - http://dx.doi.org/10.7494/OpMath.2015.35.2.171
AB  - A \(b\)-coloring is a coloring of the vertices of a graph such that each color class contains a vertex that has a neighbor in all other color classes, and the \(b\)-chromatic number \(b(G)\) of a graph \(G\) is the largest integer \(k\) such that \(G\) admits a \(b\)-coloring with \(k\) colors. A simple graph \(G\) is called \(b^{+}\)-vertex (edge) critical if the removal of any vertex (edge) of \(G\) increases its \(b\)-chromatic number. In this note, we explain some properties in \(b^{+}\)-vertex (edge) critical graphs, and we conclude with two open problems.
KW  - \(b\)-coloring
KW  - \(b\)-chromatic number
KW  - critical graphs
SN  - 1232-9274
ER  -