7 citations · 14 across the 18 of their papers we have counts for
6 papers · 1 filter
Geometric graphs with exponential chromatic number and arbitrary girth
Matija Bucić, James Davies
In 1975 Erdős initiated the study of the following very natural question. What can be said about the chromatic number of unit distance graphs in that have large girt…
On polynomial degree-boundedness
Romain Bourneuf, Matija Bucić, Linda Cook +1
We prove a conjecture of Bonamy, Bousquet, Pilipczuk, Rzążewski, Thomassé, and Walczak, that for every graph , there is a polynomial such that for every positive integer …
Essentially tight bounds for rainbow cycles in proper edge-colourings
Noga Alon, Matija Bucić, Lisa Sauermann +2
An edge-coloured graph is said to be rainbow if no colour appears more than once. Extremal problems involving rainbow objects have been a focus of much research over the last decad…
The power of many colours
Noga Alon, Matija Bucić, Micha Christoph +1
A classical problem, due to Gerencsér and Gyárfás from 1967, asks how large a monochromatic connected component can we guarantee in any -edge colouring of ? We consider how…
Unit and distinct distances in typical norms
Noga Alon, Matija Bucić, Lisa Sauermann
Erdős' unit distance problem and Erdős' distinct distances problem are among the most classical and well-known open problems in discrete mathematics. They ask for the maximum numbe…
Induced subgraph density. I. A loglog step towards Erdos-Hajnal
Matija Bucić, Tung Nguyen, Alex Scott +1
In 1977, Erdős and Hajnal made the conjecture that, for every graph , there exists such that every -free graph has a clique or stable set of size at least ;…