B. Bosek

collaborators

5 papers

math.CO2020

Reflections on the Erd\H {o}s Discrepancy Problem

Bartłomiej Bosek, Jarosław Grytczuk

We consider some coloring issues related to the famous Erd\H {o}s Discrepancy Problem. A set of the form $A_{s, k} = {s, 2 s, \dots, k s}$ , with $s, k \in N$ , is called a \emph{ho…

math.CO2020

Dilworth's Theorem for Borel Posets

Bartłomiej Bosek, Jarosław Grytczuk, Zbigniew Lonc

A famous theorem of Dilworth asserts that any finite poset of width $k$ can be decomposed into $k$ chains. We study the following problem: given a Borel poset $P$ of finite width $…

math.CO2020

Majority choosability of countable graphs

Marcin Anholcer, Bartłomiej Bosek, Jarosław Grytczuk

In any vertex coloring of a graph some edges have differently colored ends (\emph{good} edges) and some are monochromatic (\emph{bad} edges). In a proper coloring all edges are goo…

math.CO2019

Planar Posets that are Accessible from Below Have Dimension at Most 6

Csaba Biró, Bartłomiej Bosek, Heather C. Smith +3

Planar posets can have arbitrarily large dimension. However, a planar poset of height $h$ has dimension at most $192 h + 96$ , while a planar poset with $t$ minimal elements has dimens…

math.CO2019

Hat chromatic number of graphs

Bartłomiej Bosek, Andrzej Dudek, Michał Farnik +2

We study the hat chromatic number of a graph defined in the following way: there is one player at each vertex of a loopless graph $G$ , an adversary places a hat of one of $K$ color…