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Achromatic Arboricity on Complete Graphs by Araujo-Pardo, Gabriela; Rubio-Montiel, Christian is a scholarly article available to read on EtoBox.

What is Achromatic Arboricity on Complete Graphs about?

In this paper we study the {\it {achromatic arboricity}} of the complete graph. This parameter arises from the arboricity of a graph as the achromatic index arises from the chromatic index. The achromatic arboricity of a graph $G$, denoted by $A_{\alpha}(G)$, is the maximum number of colors that can be used to color the edges of $G$ such that every color class induces a forest but any two color classes contain a cycle. In particular, if $G$ is a complete graph we prove that \[\frac{1}{4}n^{\frac{3}{2}}-\Theta(n) \leq A_{\alpha}(G)\leq \frac{1}{\sqrt{2}}n^{\frac{3}{2}}-\Theta(n).\]

Author

Araujo-Pardo, Gabriela; Rubio-Montiel, Christian

Published

2021

Language

EN