10 citations · 10 across the 1 of their papers we have counts for
4 papers · 1 filter
Weak Coloring Numbers of Intersection Graphs
Zdeněk Dvořák, Jakub Pekárek, Torsten Ueckerdt +1
Weak and strong coloring numbers are generalizations of the degeneracy of a graph, where for each natural number , we seek a vertex ordering such every vertex can (weakly respec…
Coloring near-quadrangulations of the cylinder and the torus
Zdeněk Dvořák, Jakub Pekárek
Let G be a simple connected plane graph and let C_1 and C_2 be cycles in G bounding distinct faces f_1 and f_2. For a positive integer l, let r(l) denote the number of integers n s…
Irreducible 4-critical triangle-free toroidal graphs
Zdeněk Dvořák, Jakub Pekárek
The theory of Dvorak, Kral, and Thomas (2015) shows that a 4-critical triangle-free graph embedded in the torus has only a bounded number of faces of length greater than 4 and that…
On generalized choice and coloring numbers
Zdeněk Dvořák, Jakub Pekárek, Jean-Sébastien Sereni
A well-known result of Alon shows that the coloring number of a graph is bounded by a function of its choosability. We explore this relationship in a more general setting with rela…