Opuscula Math. 35, no. 2 (2015), 171-180
http://dx.doi.org/10.7494/OpMath.2015.35.2.171

Opuscula Mathematica

# On b-vertex and b-edge critical graphs

Noureddine Ikhlef Eschouf
Mostafa Blidia

Abstract. 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.

Keywords: $$b$$-coloring, $$b$$-chromatic number, critical graphs.

Mathematics Subject Classification: 05C15.

Full text (pdf)

Noureddine Ikhlef Eschouf, Mostafa Blidia, On b-vertex and b-edge critical graphs, Opuscula Math. 35, no. 2 (2015), 171-180, http://dx.doi.org/10.7494/OpMath.2015.35.2.171

a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.