SAMS Subject Classification Number: 6

Consider a graph \(G(V, E)\). A function \(\pi:V\rightarrow\{1, \ldots, k\}\) is a packing coloring of order \(k\) if \(\pi(u) = \pi(v)\) implies the distance between \(u\) and \(v\) is more than \(\pi(u)\). The minimum number of colors with which the vertices of a graph \(G\) can be packing colored is called the packing chromatic number of \(G\), denoted by \(\chi_\rho(G)\). We will discuss the packing chromatic number of various graphs with emphasis on the upper bound and the lower bound of the packing chromatic number of the 2- dimensional infinite square lattice/grid. A discussion of the packing chromatic number of the torus will follow. A comparison will be made between the packing chromatic numbers of the grid and the torus.

[1] A survey on packing colorings, B Bresar, J Ferme, S Klavzar, D F Rall, Discussiones Mathematicae Graph Theory 40, 2020, 923-970

Bio: Betsie did her undergraduate studies at UP; her graduate Studies at UJ (RAU). She taught at High School Die Fakkel (1980 – 1992) and was a lecturer/senior lecturer and associate professor at UJ (RAU) (1993 – 2016). From 2016 until now, she is employed at Wits. Betsie was HoS/Deputy HoS of Mathematics at UJ and then at Wits (18 years in total). She became full professor in March 2019.
Betsie published 23 ISI articles, supervised / co-supervised to completion 7 doctoral and 15 masters students. She presented at 32 conferences, here and overseas. She externals for universities and evaluated 7 times other schools / departments of mathematics at universities in the country.