G. Mota

activity

20152026

most citedLoose Hamiltonian cycles forced by large

(k - 2)

-degree - approximate version

15 citations · 83 across the 30 of their papers we have counts for

collaborators

36 papers

math.CO2026

An 18-colour bound for locally irregular decompositions

Carla Negri Lintzmayer, Guilherme Oliveira Mota, Maycon Sambinelli +1

A graph is locally irregular if adjacent vertices have distinct degrees. A graph G is decomposable if its edge set can be decomposed into locally irregular graphs, and its locally…

math.CO2026

Monochromatic components in dense 2-edge-coloured balanced bipartite graphs

César Bispo, George Kontogeorgiou, Marcelo Lage +2

We prove that each $2$ -edge-coloured spanning subgraph $G$ of $K_{n, n}$ with $δ (G) \geq ⌊(2 n + 1) /3 ⌋$ can be covered by at most three monochromatic components. We provide…

math.CO2026

Monochromatic cycle partitions in 3-mean edge-colourings

Csaba Biró, Richard Lang, Guilherme Oliveira Mota +4

Given $r \in N$ and an edge-coloured complete graph such that the average number of colours incident with a vertex is at most $r$ , Conlon and Stein asked whether there is…

math.CO2026

Gallai 3-colourings of random graphs

Fabrício S. Benevides, Rubens C. S. Monteiro, Guilherme O. Mota

A Gallai $k$ -colouring of a graph $G$ is a colouring of $E (G)$ with $k$ colours that induces no rainbow triangles, that is, a triangle with edges of 3 different colours. We give a…

math.CO2024

A canonical Ramsey theorem for even cycles in random graphs

José D. Alvarado, Y. Kohayakawa, Patrick Morris +1

The celebrated canonical Ramsey theorem of Erdős and Rado implies that for $2 \leq k \in N$ , any colouring of the edges of $K_{n}$ with $n$ sufficiently large gives a copy of…

math.CO2023

Resilience for Loose Hamilton Cycles

José D. Alvarado, Yoshiharu Kohayakawa, Richard Lang +2

We study the emergence of loose Hamilton cycles in subgraphs of random hypergraphs. Our main result states that the minimum $d$ -degree threshold for loose Hamiltonicity relative to…

math.CO2023

A canonical Ramsey theorem with list constraints in random (hyper-)graphs

José D. Alvarado, Yoshiharu Kohayakawa, Patrick Morris +1

The celebrated canonical Ramsey theorem of Erdős and Rado implies that for a given $k$ -uniform hypergraph (or $k$ -graph) $H$ , if $n$ is sufficiently large then any colouring of the…

math.CO2022

Directed graphs with lower orientation Ramsey thresholds

Gabriel Ferreira Barros, Bruno Pasqualotto Cavalar, Yoshiharu Kohayakawa +2

We investigate the threshold $p_{H} = p_{H} (n)$ for the Ramsey-type property $G (n, p) \to H$ , where $G (n, p)$ is the binomial random graph and $G \to H$ indicates that…

math.CO2022

Counting orientations of random graphs with no directed k-cycles

Marcelo Campos, Maurício Collares, Guilherme Oliveira Mota

For every $k \geq 3$ , we determine the order of growth, up to polylogarithmic factors, of the number of orientations of the binomial random graph containing no directed cycle of le…

math.CO2022★ 1 cited

The threshold for the constrained Ramsey property

Maurício Collares, Yoshiharu Kohayakawa, Carlos Gustavo Moreira +1

Given graphs $G$ , $H_{1}$ , and $H_{2}$ , let $G mr (H_{1}, H_{2})$ denote the property that in every edge colouring of $G$ there is a monochromatic copy of $H_{1}$ or a rain…

math.CO2022

On the anti-Ramsey threshold for non-balanced graphs

Pedro Araújo, Taísa Martins, Letícia Mattos +3

For graphs $G$ and $H$ , we write $G ⟶ rb H$ if any proper edge-coloring of $G$ contains a rainbow copy of $H$ , i.e., a copy where no color appear…

math.CO2021

Counting orientations of graphs with no strongly connected tournaments

Fábio Botler, Carlos Hoppen, Guilherme Oliveira Mota

Let $S_{k} (n)$ be the maximum number of orientations of an $n$ -vertex graph $G$ in which no copy of $K_{k}$ is strongly connected. For all integers $n$ , $k \geq 4$ where $n \geq 5$ or $k…

math.CO2020★ 1 cited

Factors in randomly perturbed hypergraphs

Yulin Chang, Jie Han, Yoshiharu Kohayakawa +2

We determine, up to a multiplicative constant, the optimal number of random edges that need to be added to a $k$ -graph $H$ with minimum vertex degree $Ω (n^{k - 1})$ to ensure an $F$ -…

math.CO2020

Covering $3$ -edge-coloured random graphs with monochromatic trees

Yoshiharu Kohayakawa, Walner Mendonça, Guilherme Oliveira Mota +1

We investigate the problem of determining how many monochromatic trees are necessary to cover the vertices of an edge-coloured random graph. More precisely, we show that for $p\gg…

math.CO2020

Anti-Ramsey threshold of cycles

Gabriel Ferreira Barros, Bruno Pasqualotto Cavalar, Guilherme Oliveira Mota +1

For graphs $G$ and $H$ , let $G ⟶ rb H$ denote the property that for every proper edge colouring of $G$ there is a rainbow copy of $H$ in $G$ . Exte…

math.CO2020★ 5 cited

Counting graph orientations with no directed triangles

Pedro Araújo, Fábio Botler, Guilherme Oliveira Mota

Alon and Yuster proved that the number of orientations of any $n$ -vertex graph in which every $K_{3}$ is transitively oriented is at most $2^{⌊ n^{2} /4 ⌋}$ for $n \geq 1 0^{4}$ …

math.CO2019★ 10 cited

The size-Ramsey number of powers of bounded degree trees

Sören Berger, Yoshiharu Kohayakawa, Giulia Satiko Maesaka +4

Given a positive integer $s$ , the $s$ -colour size-Ramsey number of a graph $H$ is the smallest integer $m$ such that there exists a graph $G$ with $m$ edges with the property that,…

math.CO2019★ 2 cited

The size-Ramsey number of 3-uniform tight paths

Jie Han, Yoshiharu Kohayakawa, Shoham Letzter +2

Given a hypergraph $H$ , the size-Ramsey number $r^_{2} (H)$ is the smallest integer $m$ such that there exists a graph $G$ with $m$ edges with the property that in any colouring…

math.CO2019★ 4 cited

Decomposing split graphs into locally irregular graphs

Carla Negri Lintzmayer, Guilherme Oliveira Mota, Maycon Sambinelli

A graph is locally irregular if any pair of adjacent vertices have distinct degrees. A locally irregular decomposition of a graph $G$ is a decomposition $D$ of $G$ such t…

math.CO2019

The anti-Ramsey threshold of complete graphs

Yoshiharu Kohayakawa, Guilherme Oliveira Mota, Olaf Parczyk +1

For graphs $G$ and $H$ , let $G {\displaystyle\smash{\begin{subarray}{c} \hbox{$\tiny\rm rb$} \\ \longrightarrow \\ \hbox{$\tiny\rm p$} \end{subarray}}}H$ denote the property that f…

math.CO2018★ 2 cited

The multicolour size-Ramsey number of powers of paths

Jie Han, Matthew Jenssen, Yoshiharu Kohayakawa +2

Given a positive integer $s$ , a graph $G$ is $s$ -Ramsey for a graph $H$ , denoted $G \to (H)_{s}$ , if every $s$ -colouring of the edges of $G$ contains a monochromatic copy of $…

math.CO2018

Counting restricted orientations of random graphs

Maurício Collares, Yoshiharu Kohayakawa, Robert Morris +1

We count orientations of $G (n, p)$ avoiding certain classes of oriented graphs. In particular, we study $T_{r} (n, p)$ , the number of orientations of the binomial random graph $G (n, p)$ …

math.CO2018

Counting Gallai 3-colorings of complete graphs

Josefran de Oliveira Bastos, Fabricio Siqueira Benevides, Guilherme Oliveira Mota +1

An edge coloring of the n-vertex complete graph K_n is a Gallai coloring if it does not contain any rainbow triangle, that is, a triangle whose edges are colored with three distinc…

math.CO2018

Three-colour bipartite Ramsey number for graphs with small bandwidth

Guilherme Oliveira Mota

We estimate the $3$ -colour bipartite Ramsey number for balanced bipartite graphs $H$ with small bandwidth and bounded maximum degree. More precisely, we show that the minimum value…

An 18-colour bound for locally irregular decompositions

Monochromatic components in dense 2-edge-coloured balanced bipartite graphs

Monochromatic cycle partitions in 3-mean edge-colourings

Gallai 3-colourings of random graphs

A canonical Ramsey theorem for even cycles in random graphs

Resilience for Loose Hamilton Cycles

A canonical Ramsey theorem with list constraints in random (hyper-)graphs

Directed graphs with lower orientation Ramsey thresholds

Counting orientations of random graphs with no directed k-cycles

The threshold for the constrained Ramsey property

On the anti-Ramsey threshold for non-balanced graphs

Counting orientations of graphs with no strongly connected tournaments

Factors in randomly perturbed hypergraphs

Covering 3-edge-coloured random graphs with monochromatic trees

Anti-Ramsey threshold of cycles

Counting graph orientations with no directed triangles

The size-Ramsey number of powers of bounded degree trees

The size-Ramsey number of 3-uniform tight paths

Decomposing split graphs into locally irregular graphs

The anti-Ramsey threshold of complete graphs

The multicolour size-Ramsey number of powers of paths

Counting restricted orientations of random graphs

Counting Gallai 3-colorings of complete graphs

Three-colour bipartite Ramsey number for graphs with small bandwidth

Covering $3$ -edge-coloured random graphs with monochromatic trees