Opuscula Math. 36, no. 5 (), 603-612
http://dx.doi.org/10.7494/OpMath.2016.36.5.603
Opuscula Mathematica

# M2-edge colorings of dense graphs

Abstract. 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.
Keywords: edge coloring, dominating set, dense graphs.
Mathematics Subject Classification: 05C15.
Cite this article as:
Jaroslav Ivančo, M2-edge colorings of dense graphs, Opuscula Math. 36, no. 5 (2016), 603-612, http://dx.doi.org/10.7494/OpMath.2016.36.5.603

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

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

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.