B. Mohar

collaborators

13 papers

math.CO2026

Genus Polynomials of Cubic Graphs with Non-Real Roots

MacKenzie Carr, Varpreet Dhaliwal, Bojan Mohar

Given a graph $G$ , its genus polynomial is $I^_{G} (x) = \sum_{k \geq 0} g_{k} (G) x^{k}$ , where $g_{k} (G)$ is the number of 2-cell embeddings of $G$ in an orientable surface of genus $k$ . The…

math.CO2026★ 3 cited

Universality in minor-closed graph classes

Tony Huynh, Bojan Mohar, Robert Å Ã¡mal +2

Stanislaw Ulam asked whether there exists a universal countable planar graph (that is, a countable planar graph that contains every countable planar graph as a subgraph). JÃ¡nos Pa…

math.CO2026

The Dominating 4-Colour Theorem

AntÃ³nio GirÃ£o, Freddie Illingworth, Bojan Mohar +6

A "dominating $K_{t}$ -model" in a graph $G$ is a sequence $(T_{1}, \dots, T_{t})$ of pairwise vertex-disjoint connected subgraphs of $G$ , such that whenever $1 \leq i < j \leq t$ every vertex…

math.CO2026

The Four Color Theorem with Linearly Many Reducible Configurations and Near-Linear Time Coloring

Yuta Inoue, Ken-ichi Kawarabayashi, Atsuyuki Miyashita +3

We give a near-linear time 4-coloring algorithm for planar graphs, improving on the previous quadratic time algorithm by Robertson et al. from 1996. Such an algorithm cannot be ach…

math.CO2026

Structure and generation of crossing-critical graphs

ZdenÄk DvoÅÃ¡k, Petr HlinÄnÃ½, Bojan Mohar

We study $c$ -crossing-critical graphs, which are the minimal graphs that require at least $c$ edge-crossings when drawn in the plane. For $c = 1$ there are only two such graphs witho…

math.CO2026

Long cycles in vertex transitive digraphs

Matija BuciÄ, Kevin Hendrey, Bojan Mohar +2

One of the most well-known conjectures concerning Hamiltonicity in graphs asserts that any sufficiently large connected vertex transitive graph contains a Hamilton cycle. In this f…