C. Thomassen

collaborators

4 papers

math.CO2020

Locally Hamiltonian graphs and minimal size of maximal graphs on a surface

James Davies, Carsten Thomassen

We prove that every locally Hamiltonian graph with $n \geq 3$ vertices and possibly with multiple edges has at least $3 n - 6$ edges with equality if and only if it triangulates the sph…

math.CO2018

Planar Ramsey graphs

Maria Axenovich, Carsten Thomassen, Ursula Schade +1

We say that a graph $H$ is planar unavoidable if there is a planar graph $G$ such that any red/blue coloring of the edges of $G$ contains a monochromatic copy of $H$ , otherwise we…

math.CO2017

The square of a planar cubic graph is $7$ -colorable

Carsten Thomassen

We prove the conjecture made by G.Wegner in 1977 that the square of every planar, cubic graph is $7$ -colorable. Here, $7$ cannot be replaced by $6$ .

math.CO2016

Decomposing graphs into a constant number of locally irregular subgraphs

Julien Bensmail, Martin Merker, Carsten Thomassen

A graph is locally irregular if no two adjacent vertices have the same degree. The irregular chromatic index $χ_{irr}^{'} (G)$ of a graph $G$ is the smallest number of locally irre…

Locally Hamiltonian graphs and minimal size of maximal graphs on a surface

Planar Ramsey graphs

The square of a planar cubic graph is 7-colorable

Decomposing graphs into a constant number of locally irregular subgraphs

The square of a planar cubic graph is $7$ -colorable