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Erdős--Pósa property of cycles that are far apart
Vida Dujmović, Gwenaël Joret, Piotr Micek +1
We prove that there exist functions such that for all nonnegative integers and , for every graph , either contains cycles such that…
Centered colorings in minor-closed graph classes
Jędrzej Hodor, Hoang La, Piotr Micek +1
A vertex coloring of a graph is -centered if for every connected subgraph of , either uses more than colors on , or there is a color that appears exact…
Planar graphs in blowups of fans
Marc Distel, Vida Dujmović, Gwenaël Joret +3
We show that every -vertex planar graph is contained in the graph obtained from a fan by blowing up each vertex by a complete graph of order . Equivalently,…
Weak coloring numbers of minor-closed graph classes
Jędrzej Hodor, Hoang La, Piotr Micek +1
We study the growth rate of weak coloring numbers of graphs excluding a fixed graph as a minor. Van den Heuvel et al. (European J. of Combinatorics, 2017) showed that for a fixed g…
Vertex Ranking of Degenerate Graphs
John Iacono, Piotr Micek, Pat Morin +1
An -vertex-ranking of a graph is a colouring of the vertices of with integer colours so that in any connected subgraph of with diameter at most , there…
Quickly excluding an apex-forest
Jędrzej Hodor, Hoang La, Piotr Micek +1
We give a short proof that for every apex-forest on at least two vertices, graphs excluding as a minor have layered pathwidth at most . This improves upon a resu…
Tight bound for the Erdős-Pósa property of tree minors
Vida Dujmović, Gwenaël Joret, Piotr Micek +1
Let be a tree on vertices. We prove that for every positive integer and every graph , either contains pairwise vertex-disjoint subgraphs each having a mi…