pseudoachromatic

pseudo- +‎ achromatic

pseudoachromatic (not comparable)

1. Partially achromatic
   • 2015, G. Araujo-Pardo, J.J. Montellano-Ballesteros, C. Rubio-Montiel, R. Strausz, “On the pseudoachromatic index of the complete graph III”, in arXiv‎:

     Let ${\displaystyle \Pi _{q}}$ be the projective plane of order ${\displaystyle q}$, let ${\displaystyle \psi (m):=\psi (L(K_{m}))}$ the pseudoachromatic number of the complete line graph of order ${\displaystyle m}$, let ${\displaystyle a\in \{3,4,\dots ,{\tfrac {q}{2}}+1\}}$ and ${\displaystyle m_{a}=(q+1)^{2}-a}$. In this paper, we improve the upper bound of ${\displaystyle \psi (m)}$ given by Araujo-Pardo et al. [J Graph Theory 66 (2011), 89--97] and Jamison [Discrete Math. 74 (1989), 99--115] in the following values: if ${\displaystyle x\geq 2}$ is an integer and ${\displaystyle m\in \{4x^{2}-x,\dots ,4x^{2}+3x-3\}}$ then ${\displaystyle \psi (m)\leq 2x(m-x-1)}$. On the other hand, if ${\displaystyle q}$ is even and there exists ${\displaystyle \Pi _{q}}$ we give a complete edge-colouring of ${\displaystyle K_{m_{a}}}$ with ${\displaystyle (m_{a}-a)q}$ colours.