189 citations · 374 across the 14 of their papers we have counts for
16 papers
Uniquely hamiltonian graphs for many sets of degrees
Gunnar Brinkmann, Matthias De Pauw
We give constructive proofs for the existence of uniquely hamiltonian graphs for various sets of degrees. We give constructions for all sets with minimum 2 (a trivial case added fo…
On Local Operations that Preserve Symmetries and on Preserving Polyhedrality of Embeddings
Gunnar Brinkmann, Heidi Van den Camp
We prove that local operations that preserve all symmetries, as e.g. dual, truncation, ambo, or join,, as well as local operations that preserve all symmetries except orientation r…
The Minimality of the Georges-Kelmans Graph
Gunnar Brinkmann, Jan Goedgebeur, Brendan D. McKay
In 1971, Tutte wrote in an article that "it is tempting to conjecture that every 3-connected bipartite cubic graph is hamiltonian". Motivated by this remark, Horton constructed a c…
On the genera of polyhedral embeddings of cubic graph
Gunnar Brinkmann, Thomas Tucker, Nico Van Cleemput
In this article we present theoretical and computational results on the existence of polyhedral embeddings of graphs. The emphasis is on cubic graphs. We also describe an efficient…
A simple and elementary proof of Whitney's unique embedding theorem
Gunnar Brinkmann
In this note we give a short and elementary proof of a more general version of Whitney's theorem that 3-connected planar graphs have a unique embedding in the plane. A consequence…
A Practical Algorithm for the Computation of the Genus
G. Brinkmann
We describe a practical algorithm to compute the (oriented) genus of a graph, give results of the program implementing this algorithm, and compare the performance to existing algor…