31 citations · 256 across the 67 of their papers we have counts for
8 papers · 1 filter
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…
On fractional fragility rates of graph classes
Zdeněk Dvořák, Jean-Sébastien Sereni
We consider, for every positive integer , probability distributions on subsets of vertices of a graph with the property that every vertex belongs to the random set sampled from…
Bounding the number of cycles in a graph in terms of its degree sequence
Zdeněk Dvořák, Natasha Morrison, Jonathan A. Noel +2
We give an upper bound on the number of cycles in a simple graph in terms of its degree sequence, and apply this bound to resolve several conjectures of Király and Arman and Tsatur…
Coloring count cones of planar graphs
Zdeněk Dvořák, Bernard Lidický
For a plane near-triangulation with the outer face bounded by a cycle , let denote the function that to each -coloring of assigns the number of ways $…
Bounded maximum degree conjecture holds precisely for -crossing-critical graphs with
Drago Bokal, Zdeněk Dvořák, Petr Hliněný +3
We study -crossing-critical graphs, which are the minimal graphs that require at least edge-crossings when drawn in the plane. For every fixed pair of integers with $c\ge 13…
Flexibility of planar graphs of girth at least six
Zdeněk Dvořák, Tomáš Masařík, Jan Musílek +1
Let G be a planar graph with a list assignment L. Suppose a preferred color is given for some of the vertices. We prove that if G has girth at least six and all lists have size at…