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

On b-vertex and b-edge critical graphs



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.
Cite this article as:
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
 
Download this article's citation as:
a .bib file (BibTeX), a .ris file (RefMan), a .enw file (EndNote)
or export to RefWorks.

RSS Feed

horizontal rule

ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
Copyright © 2003−2017 OPUSCULA MATHEMATICA
Contact: opuscula@agh.edu.pl
Made by Tomasz Zabawa

horizontal rule

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.