2021/03/22 by Araujo-Pardo, Gabriela, Rubio-Montiel, Christian
#05C15 #51E15 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2103.12225
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 Aα(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 (1)/(4)n(3)/(2)-Θ(n) ≤ Aα(G)≤ (1)/(√(2))n(3)/(2)-Θ(n).