On L(h,k)-labelings of oriented graphs - Colucci, Lucas (Anais do Encontro de Teoria da Computação (ETC), 2021)
We compare the behaviour of the $L(h,k)$-number of undirected and oriented graphs in terms of maximum degree, highlighting differences between the two contexts. In particular, we prove that, for every $h$ and $k$, oriented graphs with bounded degree in every block of their underlying graph (for instance, oriented trees and oriented cacti) have bounded $L(h,k)$-number, giving an upper bound on this number which is sharp up to a multiplicative factor $4$.