3 citations · 6 across the 7 of their papers we have counts for
10 papers
Counting edge-colorings of a complete graph avoiding a rainbow
Fabricio S. Benevides, Josefran de O. Bastos
For natural numbers let be the number of -edge-colorings of that do not contain a rainbow copy of a , that is, a copy of in which all e…
Gallai 3-colourings of random graphs
Fabrício S. Benevides, Rubens C. S. Monteiro, Guilherme O. Mota
A Gallai -colouring of a graph is a colouring of with colours that induces no rainbow triangles, that is, a triangle with edges of 3 different colours. We give a…
Partitioning 2-edge-coloured bipartite graphs into monochromatic cycles
Fabrício Siqueira Benevides, Arthur Lima Quintino, Alexandre Talon
Given an -edge-colouring of the edges of a graph , we say that it can be partitioned into monochromatic cycles when there exists a set of vertex-disjoint monochromati…
Maximizing the expected number of components in an online search of a graph
Fabrício Siqueira Benevides, Małgorzata Sulkowska
The following optimal stopping problem is considered. The vertices of a graph are revealed one by one, in a random order, to a selector. He aims to stop this process at a time…
The number of Gallai k-colorings of complete graphs
Josefran de Oliveira Bastos, Fabricio S. Benevides, Jie Han
An edge coloring of the -vertex complete graph, , is a Gallai coloring if it does not contain any rainbow triangle, that is, a triangle whose edges are colored with three d…
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…
Edge-colorings of graphs avoiding complete graphs with a prescribed coloring
Fabricio S. Benevides, Carlos Hoppen, Rudini Menezes Sampaio
Given a graph and an integer , a partition of the edge set of into at most classes, and a graph , define as the number…
Circular Backbone Colorings: on matching and tree backbones of planar graphs
Julio Araujo, Fabricio Benevides, Alexandre Cezar +1
Given a graph , and a spanning subgraph of , a circular -backbone -coloring of is a proper -coloring of such that $q\le \lvert c(u)-c(v)\rvert \l…
Generalising separating families of fixed size
Fabrício S. Benevides, Dániel Gerbner, Cory T. Palmer +1
We examine the following version of a classic combinatorial search problem introduced by Rényi: Given a finite set of elements we want to identify an unknown subset $Y \sub…
Maximum percolation time in two-dimensional bootstrap percolation
Fabricio Benevides, Michał Przykucki
We consider a classic model known as bootstrap percolation on the square grid. To each vertex of the grid we assign an initial state, infected or healthy, and then in…