Kamil Popielarz

activity

20162019

most citedGeneralised Majority Colourings of Digraphs

7 citations · 7 across the 2 of their papers we have counts for

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9 papers · 1 filter

math.CO2019

$(2 k + 1)$ -connected tournaments with large minimum out-degree are $k$ -linked

António Girão, Kamil Popielarz, Richard Snyder

Pokrovskiy conjectured that there is a function $f : N \to N$ such that any $2 k$ -strongly-connected tournament with minimum out and in-degree at least $f(k…

math.CO2019

Subdivisions of digraphs in tournaments

António Girão, Kamil Popielarz, Richard Snyder

We show that for every positive integer $k$ , any tournament with minimum out-degree at least $(2 + o (1)) k^{2}$ contains a subdivision of the complete directed graph on $k$ vertices, wh…

math.CO2017

Rainbow saturation of graphs

António Girão, David Lewis, Kamil Popielarz

In this paper we study the following problem proposed by Barrus, Ferrara, Vandenbussche, and Wenger. Given a graph $H$ and an integer $t$ , what is $\operatorname{sat}_{t}\left(n, \…

math.CO2017

Partite Saturation of Complete Graphs

António Girão, Teeradej Kittipassorn, Kamil Popielarz

We study the problem of determining $s a t (n, k, r)$ , the minimum number of edges in a $k$ -partite graph $G$ with $n$ vertices in each part such that $G$ is $K_{r}$ -free but the addition…

math.CO2017

On the maximum diameter of path-pairable graphs

Antonio Girao, Gabor Meszaros, Kamil Popielarz +1

A graph is path-pairable if for any pairing of its vertices there exist edge disjoint paths joining the vertices in each pair. We obtain sharp bounds on the maximum possible diamet…

math.CO2017

Large induced subgraphs with $k$ vertices of almost maximum degree

António Girão, Kamil Popielarz

In this note we prove that for every integer $k$ , there exist constants $g_{1} (k)$ and $g_{2} (k)$ such that the following holds. If $G$ is a graph on $n$ vertices with maximum degr…

math.CO2017

On the maximum degree of path-pairable planar graphs

António Girão, Gábor Mészáros, Kamil Popielarz +1

A graph is path-pairable if for any pairing of its vertices there exist edge-disjoint paths joining the vertices in each pair. We investigate the behaviour of the maximum degree in…

math.CO2017★ 7 cited

Generalised Majority Colourings of Digraphs

António Girão, Teeradej Kittipassorn, Kamil Popielarz

The purpose of this note is to draw attention to problems related to a concept called majority colouring recently studied by Kreutzer, Oum, Seymour, van der Zypen and Wood. They ra…

math.CO2016

A Stability Theorem for Maximal $K_{r + 1}$ -free Graphs

Kamil Popielarz, Julian Sahasrabudhe, Richard Snyder

For $r \geq 2$ , we show that every maximal $K_{r + 1}$ -free graph $G$ on $n$ vertices with $(1 - \frac{1}{r}) \frac{n ^{2}}{2} - o (n^{\frac{r + 1}{r}})$ edges contains a complete $r$ -partite s…

(2k+1)-connected tournaments with large minimum out-degree are k-linked

Subdivisions of digraphs in tournaments

Rainbow saturation of graphs

Partite Saturation of Complete Graphs

On the maximum diameter of path-pairable graphs

Large induced subgraphs with k vertices of almost maximum degree

On the maximum degree of path-pairable planar graphs

Generalised Majority Colourings of Digraphs

A Stability Theorem for Maximal Kr+1​-free Graphs

$(2 k + 1)$ -connected tournaments with large minimum out-degree are $k$ -linked

Large induced subgraphs with $k$ vertices of almost maximum degree

A Stability Theorem for Maximal $K_{r + 1}$ -free Graphs