Laura Gellert

activity

20152017

collaborators

6 papers

math.CO2017

Cycle decompositions of pathwidth-6 graphs

Elke Fuchs, Laura Gellert, Irene Heinrich

Hajós conjecture asserts that a simple Eulerian graph on n vertices can be decomposed into at most (n - 1)/2 cycles. The conjecture is only proved for graph classes in which every…

math.CO2017

On $t$ -perfect triangulations of the projective plane

Elke Fuchs, Laura Gellert

We prove that a triangulation of the projective plane is (strongly) $t$ -perfect if and only if it is perfect and contains no $K_{4}$ .

math.CO2016

Reducing quadrangulations of the sphere and the projective plane

Elke Fuchs, Laura Gellert

We show that every quadrangulation of the sphere can be transformed into a $4$ -cycle by deletions of degree- $2$ vertices and by $t$ -contractions at degree- $3$ vertices. A $t$ -contr…

math.CO2016

Chromatic index, treewidth and maximum degree

Henning Bruhn, Laura Gellert, Richard Lang

We conjecture that any graph $G$ with treewidth~ $k$ and maximum degree $Δ (G) \geq k + k$ satisfies $χ^{'} (G) = Δ (G)$ . In support of the conjecture we prove its fractional version.…

math.CO2015

On degree sequences of undirected, directed, and bidirected graphs

Laura Gellert, Raman Sanyal

Bidirected graphs generalize directed and undirected graphs in that edges are oriented locally at every node. The natural notion of the degree of a node that takes into account (lo…

math.CO2015

Jacobsthal numbers in generalised Petersen graphs

Henning Bruhn, Laura Gellert, Jacob Günther

We prove that the number of $1$ -factorisations of a generalised Petersen graph of the type $GP (3 k, k)$ is equal to the $k$ th Jacobsthal number $J (k)$ if $k$ is odd, and equal to $4J…