Publications - Published papers

Please find below publications of our group. Currently, we list 508 papers. Some of the publications are in collaboration with the group of Sonja Prohaska and are also listed in the publication list for her individual group. Access to published papers (access) is restricted to our local network and chosen collaborators. If you have problems accessing electronic information, please let us know:

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Diagonalized Cartesian Products of S-prime graphs are S-prime

Marc Hellmuth, Lydia Gringmann, Peter F. Stadler


PREPRINT 09-035: [ PDF ]


Discrete Mathematics 312:74–80 (2012)


A graph is said to be S-prime if, whenever it is a subgraph of a nontrivial Cartesian product graph, it is a subgraph of one of the factors. A diagonalized Cartesian product is obtained from a Cartesian product graph by connecting two vertices of maximal distance by an additional edge. We show there that a diagonalized product of S-prime graphs is again S-prime. Klav{\v{z}}ar \emph{et al.} [\emph{Discr.\ Math.} \textbf{244}: 223-230 (2002)] proved that a graph is S-prime if and only if it admits a nontrivial path-$k$-coloring. We derive here a characterization of all path-$k$-colorings of Cartesian products of S-prime graphs.


S-prime, diagonalized Cartesian product, path-k-coloring