On the Partial Grundy Number of a Graph Minus a Matching

  • Kenny Domingues UFC
  • Ana Silva UFC


Given a k-coloring S1, . . . , Sk of G, a vertex in Si is said to be greedy if it has neighbors in Sj, for every j < i. Thus, a Grundy coloring can be seen as a coloring where every vertex is greedy. In contrast, a partial Grundy coloring is defined as a coloring in which each color class has at least one greedy vertex; the maximum number of colors in a partial Grundy coloring is denoted by ∂Γ(G). In this paper, we investigate some conjectures about Grundy colorings, already known not to hold, adapted to partial Grundy colorings. We prove that, while two of them also do not hold, a third does. Namely, that given a graph G and a matching M of G, we have that ∂Γ(G) ≤ 2∂Γ(G − M).

Palavras-chave: Grundy coloring, Partial Grundy coloring


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DOMINGUES, Kenny; SILVA, Ana. On the Partial Grundy Number of a Graph Minus a Matching. In: ENCONTRO DE TEORIA DA COMPUTAÇÃO (ETC), 7. , 2022, Niterói. Anais [...]. Porto Alegre: Sociedade Brasileira de Computação, 2022 . p. 97-100. ISSN 2595-6116. DOI: https://doi.org/10.5753/etc.2022.223134.