Meaning of pseudoachromatic | Babel Free

Definitions

Partially achromatic

not-comparable

Examples

“Let #92;Pi#95;q be the projective plane of order q, let #92;psi(m)#58;#61;#92;psi(L(K#95;m)) the pseudoachromatic number of the complete line graph of order m, let a#92;in#92;#123;3,4,#92;dots,#92;tfrac#123;q#125;#123;2#125;#43;1#92;#125; and m#95;a#61;(q#43;1)²-a. In this paper, we improve the upper bound of #92;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#92;geq 2 is an integer and m#92;in#92;#123;4x²-x,#92;dots,4x²#43;3x-3#92;#125; then #92;psi(m)#92;leq 2x(m-x-1). On the other hand, if q is even and there exists #92;Pi#95;q we give a complete edge-colouring of K#95;#123;m#95;a#125; with (m#95;a-a)q colours.”

CEFR level