Zdeněk Dvořák

activity

20222026

collaborators

3 papers

math.CO2026

Every graph with no $K_{7}^{=}$ minor is 6-colorable

Zdeněk Dvořák, Sergey Norin, Neil Rahman

The first open case of Hadwiger's conjecture states that every $K_{7}$ -minor-free graph is 6-colorable. We prove that this is the case for $K_{7}^{=}$ -minor-free graphs, where $K_{7}^{=}$ de…

math.CO2023

Solution to a problem of Grünbaum on the edge density of $4$ -critical planar graphs

Zdeněk Dvořák, Carl Feghali

We show that $lim sup ∣ E (G) ∣/∣ V (G) ∣ = 2.5$ over all $4$ -critical planar graphs $G$ , answering a question of Grünbaum from 1988.

math.CO2022

Asymptotic dimension of intersection graphs

Zdeněk Dvořák, Sergey Norin

We show that intersection graphs of compact convex sets in R^n of bounded aspect ratio have asymptotic dimension at most 2n+1. More generally, we show this is the case for intersec…

Every graph with no K7=​ minor is 6-colorable

Solution to a problem of Grünbaum on the edge density of 4-critical planar graphs

Asymptotic dimension of intersection graphs

Every graph with no $K_{7}^{=}$ minor is 6-colorable

Solution to a problem of Grünbaum on the edge density of $4$ -critical planar graphs