58 citations · 549 across the 45 of their papers we have counts for
5 papers · 2 filters
(4,2)-choosability of planar graphs with forbidden structures
Zhanar Berikkyzy, Christopher Cox, Michael Dairyko +8
All planar graphs are 4-colorable and 5-choosable, while some planar graphs are not 4-choosable. Determining which properties guarantee that a planar graph can be colored using lis…
On the Strong Chromatic Index of Sparse Graphs
Philip DeOrsey, Jennifer Diemunsch, Michael Ferrara +7
The strong chromatic index of a graph , denoted , is the least number of colors needed to edge-color so that edges at distance at most two receive distinct colors.…
Fine structure of 4-critical triangle-free graphs II. Planar triangle-free graphs with two precolored 4-cycles
Zdeněk Dvořák, Bernard Lidický
We study 3-coloring properties of triangle-free planar graphs with two precolored 4-cycles and that are far apart. We prove that either every precoloring of $C_1\cu…
Fine structure of 4-critical triangle-free graphs III. General surfaces
Zdeněk Dvořák, Bernard Lidický
Dvořák, Král' and Thomas gave a description of the structure of triangle-free graphs on surfaces with respect to 3-coloring. Their description however contains two substructures (b…
Fine structure of 4-critical triangle-free graphs I. Planar graphs with two triangles and 3-colorability of chains
Zdeněk Dvořák, Bernard Lidický
Aksenov proved that in a planar graph G with at most one triangle, every precoloring of a 4-cycle can be extended to a 3-coloring of G. We give an exact characterization of planar…