pseudoachromatic

English

Etymology

pseudo- +‎ achromatic

Adjective

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^[1]:

     Let $\Pi _{q}$ be the projective plane of order $q$, let $\psi (m):=\psi (L(K_{m}))$ the pseudoachromatic number of the complete line graph of order $m$, let $a\in \{3,4,\dots ,{\tfrac {q}{2}}+1\}$ and $m_{a}=(q+1)^{2}-a$. In this paper, we improve the upper bound of $\psi (m)$ 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 $x\geq 2$ is an integer and $m\in \{4x^{2}-x,\dots ,4x^{2}+3x-3\}$ then $\psi (m)\leq 2x(m-x-1)$. On the other hand, if $q$ is even and there exists $\Pi _{q}$ we give a complete edge-colouring of $K_{m_{a}}$ with $(m_{a}-a)q$ colours.