31 citations · 256 across the 67 of their papers we have counts for
11 papers · 1 filter
Large Independent Sets in Triangle-Free Planar Graphs
Zdenek Dvorak, Matthias Mnich
Every triangle-free planar graph on n vertices has an independent set of size at least (n+1)/3, and this lower bound is tight. We give an algorithm that, given a triangle-free plan…
Immersion in four-edge-connected graphs
Maria Chudnovsky, Zdeněk Dvořák, Tereza Klimošová +1
Fix g>1. Every graph of large enough tree-width contains a g x g grid as a minor; but here we prove that every four-edge-connected graph of large enough tree-width contains a g x g…
Dynamic Data Structure for Tree-Depth Decomposition
Zdenek Dvorak, Martin Kupec, Vojtech Tuma
We present a dynamic data structure for representing a graph with tree-depth at most . Tree-depth is an important graph parameter which arose in the study of sparse graph cl…
Planar 4-critical graphs with four triangles
Oleg V. Borodin, Zdeněk Dvořák, Alexandr V. Kostochka +2
By the Grunbaum-Aksenov Theorem (extending Grotzsch's Theorem) every planar graph with at most three triangles is 3-colorable. However, there are infinitely many planar 4-critical…
3-coloring triangle-free planar graphs with a precolored 8-cycle
Zdeněk Dvořák, Bernard Lidický
Let G be a planar triangle-free graph and let C be a cycle in G of length at most 8. We characterize all situations where a 3-coloring of C does not extend to a proper 3-coloring o…
4-critical graphs on surfaces without contractible (<=4)-cycles
Zdeněk Dvořák, Bernard Lidický
We show that if G is a 4-critical graph embedded in a fixed surface so that every contractible cycle has length at least 5, then G can be expressed as $G=G'\cup G_1\cup G_2\cup…