5 citations · 12 across the 13 of their papers we have counts for
14 papers
Marshall Quotients of the Rings
Lucas Colucci, Mathuzalem Ferreira de Lima, Kaique Matias de Andrade Roberto
We study the Marshall quotient \[ M(n)=M(\mathbb Z/n\mathbb Z) \] obtained from the ring of integers modulo by quotienting by the square classes of non-zero-divisors. Using ele…
On converse invariant trees of diameter four
Fernando Afonso, Lucas Colucci, Tássio Naia
Let be an oriented graph, and let denote the number of copies of in a tournament . We say that is \emph{converse invariant} if for…
A linear upper bound on the zero-sum Ramsey number of forests in
Lucas Colucci, Marco D'Emidio
Let be a positive integer and let be a graph. The zero-sum Ramsey number is the least integer (if it exists) such that for every edge-coloring $χ\,…
On Modular Edge Colourings of Graphs
Gaétan Berthe, Marthe Bonamy, Fábio Botler +5
Given a graph and an integer , let denote the minimum number of colours required to colour the edges of such that, in each colour class, the subgraph ind…
On a problem of Caro on -Ramsey number of forests
José D. Alvarado, Lucas Colucci, Roberto Parente
Let be a positive integer and let be a graph. The zero-sum Ramsey number is the least integer (if it exists) such that for every edge-coloring $χ\,…
The chromatic index of random graphs
Fábio Botler, Lucas Colucci, Yoshiharu Kohayakawa
The chromatic index of a graph is the minimum number of colors needed to color the edges of in a way that the subgraph spanned by the edges of each color has…
On the Erdős-Sloane and Shifted Sloane Persistence Problems
Gabriel Bonuccelli, Lucas Colucci, Edson de Faria
In this paper, we investigate two variations on the so-called persistence problem of Sloane: the shifted version, which was introduced by Wagstaff; and the nonzero version, propose…
The mod chromatic index of graphs is
Fábio Botler, Lucas Colucci, Yoshiharu Kohayakawa
Let denote the minimum number of colors needed to color the edges of a graph in a way that the subgraph spanned by the edges of each color has all degrees congruent t…
On L(2,1)-labelings of some products of oriented cycles
Lucas Colucci, Ervin Győri
We refine two results of Jiang, Shao and Vesel on the -labeling number of the Cartesian and the strong product of two oriented cycles. For the Cartesian product, we com…
Edge colorings of graphs without monochromatic stars
Lucas Colucci, Ervin Győri, Abhishek Methuku
In this note, we improve on results of Hoppen, Kohayakawa and Lefmann about the maximum number of edge colorings without monochromatic copies of a star of a fixed size that a graph…
On L(2,1)-labelings of oriented graphs
Lucas Colucci, Ervin Győri
We extend a result of Griggs and Yeh about the maximum possible value of the L(2,1)-labeling number of a graph in terms of its maximum degree to oriented graphs. We consider the pr…
Terminal-Pairability in Complete Bipartite Graphs with Non-Bipartite Demands
Lucas Colucci, Péter L. Erdős, Ervin Győri +1
We investigate the terminal-pairability problem in the case when the base graph is a complete bipartite graph, and the demand graph is a (not necessarily bipartite) multigraph on t…
Terminal-Pairability in Complete Bipartite Graphs
Lucas Colucci, Péter L. Erdős, Ervin Győri +1
We investigate the terminal-pairibility problem in the case when the base graph is a complete bipartite graph, and the demand graph is also bipartite with the same color classes. W…
Coloring 2-intersecting hypergraphs
Lucas Colucci, András Gyárfás
A hypergraph is 2-intersecting if any two edges intersect in at least two vertices. Blais, Weinstein and Yoshida asked (as a first step to a more general problem) whether every 2-i…