On L(h,k)-labelings of oriented graphs


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 $4$.
Palavras-chave: graph labeling, L(2,1)-labeling, graph theory


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COLUCCI, Lucas. On L(h,k)-labelings of oriented graphs. In: ENCONTRO DE TEORIA DA COMPUTAÇÃO (ETC), 6. , 2021, Evento Online. Anais [...]. Porto Alegre: Sociedade Brasileira de Computação, 2021 . p. 66-69. ISSN 2595-6116. DOI: https://doi.org/10.5753/etc.2021.16382.