pseudoachromatic

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:

     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.