16 citations · 45 across the 6 of their papers we have counts for
9 papers · 1 filter
A rainbow version of Lehel's conjecture
Pedro Araújo, Xiao-Chuan Liu, Taísa Martins +4
Lehel's conjecture states that every 2-edge-colouring of K_n admits a partition of its vertex set into two monochromatic cycles. It was proven for sufficiently large n by Łuczak, R…
A lower bound for set-colouring Ramsey numbers
Lucas Aragão, Maurício Collares, João Pedro Marciano +2
The set-colouring Ramsey number is defined to be the minimum such that if each edge of the complete graph is assigned a set of colours from $\{1,\ldots,r…
On the anti-Ramsey threshold for non-balanced graphs
Pedro Araújo, Taísa Martins, Letícia Mattos +3
For graphs and , we write if any proper edge-coloring of contains a rainbow copy of , i.e., a copy where no color appear…
Weak saturation numbers of complete bipartite graphs in the clique
Gal Kronenberg, Taísa Martins, Natasha Morrison
The notion of weak saturation was introduced by Bollobás in 1968. Let and be graphs. A spanning subgraph is weakly -saturated if it contains no copy…
No additional tournaments are quasirandom-forcing
Robert Hancock, Adam Kabela, Daniel Kral +4
A tournament H is quasirandom-forcing if the following holds for every sequence (G_n) of tournaments of growing orders: if the density of H in G_n converges to the expected density…
The size-Ramsey number of powers of bounded degree trees
Sören Berger, Yoshiharu Kohayakawa, Giulia Satiko Maesaka +4
Given a positive integer , the -colour size-Ramsey number of a graph is the smallest integer such that there exists a graph with edges with the property that,…
The step Sidorenko property and non-norming edge-transitive graphs
Daniel Král', Taísa Martins, Péter Pál Pach +1
Sidorenko's Conjecture asserts that every bipartite graph H has the Sidorenko property, i.e., a quasirandom graph minimizes the density of H among all graphs with the same edge den…
Decomposing graphs into edges and triangles
Daniel Král', Bernard Lidický, Taísa L. Martins +1
We prove the following 30-year old conjecture of Győri and Tuza: the edges of every -vertex graph can be decomposed into complete graphs of orders two an…
Finitely forcible graph limits are universal
Jacob W. Cooper, Daniel Kral, Taisa L. Martins
The theory of graph limits represents large graphs by analytic objects called graphons. Graph limits determined by finitely many graph densities, which are represented by finitely…