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Exponentially many Z5-colorings in simple planar graphs
Rikke Langhede, Carsten Thomassen
Every planar simple graph with n vertices has at least 2^(n/9) Z5-colorings.
Group connectivity and group coloring: small groups versus large groups
Rikke Langhede, Carsten Thomassen
A well-known result of Tutte says that if Gamma is an Abelian group and G is a graph having a nowhere-zero Gamma-flow, then G has a nowhere-zero Gamma'-flow for each Abelian group…
Locally Hamiltonian graphs and minimal size of maximal graphs on a surface
James Davies, Carsten Thomassen
We prove that every locally Hamiltonian graph with vertices and possibly with multiple edges has at least edges with equality if and only if it triangulates the sph…
Planar Ramsey graphs
Maria Axenovich, Carsten Thomassen, Ursula Schade +1
We say that a graph is planar unavoidable if there is a planar graph such that any red/blue coloring of the edges of contains a monochromatic copy of , otherwise we…
The square of a planar cubic graph is -colorable
Carsten Thomassen
We prove the conjecture made by G.Wegner in 1977 that the square of every planar, cubic graph is -colorable. Here, cannot be replaced by .
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 of a graph is the smallest number of locally irre…