Milos Trujic

activity

20172022

most citedLocal resilience of an almost spanning

k

-cycle in random graphs

2 citations · 2 across the 3 of their papers we have counts for

collaborators

8 papers

math.CO2022

Ramsey numbers for multiple copies of sparse graphs

Aurelio Sulser, Miloš Trujić

For a graph $H$ and an integer $n$ , we let $n H$ denote the disjoint union of $n$ copies of $H$ . In 1975, Burr, Erdős, and Spencer initiated the study of Ramsey numbers for $n H$ , on…

math.CO2022

Transference for loose Hamilton cycles in random $3$ -uniform hypergraphs

Kalina Petrova, Miloš Trujić

A loose Hamilton cycle in a hypergraph is a cyclic sequence of edges covering all vertices in which only every two consecutive edges intersect and do so in exactly one vertex. With…

math.CO2021

The size-Ramsey number of cubic graphs

David Conlon, Rajko Nenadov, Miloš Trujić

We show that the size-Ramsey number of any cubic graph with $n$ vertices is $O (n^{8/5})$ , improving a bound of $n^{5/3 + o (1)}$ due to Kohayakawa, Rödl, Schacht, and Szemerédi. The…

math.CO2020

Covering cycles in sparse graphs

Frank Mousset, Nemanja Škorić, Miloš Trujić

Let $k \geq 2$ be an integer. Kouider and Lonc proved that the vertex set of every graph $G$ with $n \geq n_{0} (k)$ vertices and minimum degree at least $n / k$ can be covered by $k -…

math.CO2018

Triangle resilience of the square of a Hamilton cycle in random graphs

Manuela Fischer, Nemanja Škorić, Angelika Steger +1

Since first introduced by Sudakov and Vu in 2008, the study of resilience problems in random graphs received a lot of attention in probabilistic combinatorics. Of particular intere…

math.CO2018

On resilience of connectivity in the evolution of random graphs

Luc Haller, Miloš Trujić

In this note we establish a resilience version of the classical hitting time result of Bollobás and Thomason regarding connectivity. A graph $G$ is said to be $α$ -resilient with re…

math.CO2017

Resilience of Perfect Matchings and Hamiltonicity in Random Graph Processes

Rajko Nenadov, Angelika Steger, Miloš Trujić

Let ${G_{i}}$ be the random graph process: starting with an empty graph $G_{0}$ with $n$ vertices, in every step $i \geq 1$ the graph $G_{i}$ is formed by taking an edge chosen uniform…

math.CO2017★ 2 cited

Local resilience of an almost spanning $k$ -cycle in random graphs

Nemanja Škorić, Angelika Steger, Miloš Trujić

The famous Pósa-Seymour conjecture, confirmed in 1998 by Komlós, Sárközy, and Szemerédi, states that for any $k \geq 2$ , every graph on $n$ vertices with minimum degree $kn/(k + 1)…