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A Systematic Approach to Crossing Numbers of Cartesian Products with Paths
Zayed Asiri, Ryan Burdett, Markus Chimani +3
Determining the crossing numbers of Cartesian products of small graphs with arbitrarily large paths has been an ongoing topic of research since the 1970s. Doing so requires the est…
Binary Programming Formulations for the Upper Domination Problem
Ryan Burdett, Michael Haythorpe, Alex Newcombe
We consider Upper Domination, the problem of finding the minimal dominating set of maximum cardinality. Very few exact algorithms have been described for solving Upper Domination.…
Variants of the Domination Number for Flower Snarks
Ryan Burdett, Michael Haythorpe, Alex Newcombe
We consider the flower snarks, a widely studied infinite family of 3--regular graphs. For the Flower snark on vertices, it is trivial to show that the domination number…
An improved binary programming formulation for the secure domination problem
Ryan Burdett, Michael Haythorpe
The secure domination problem, a variation of the domination problem with some important real-world applications, is considered. Very few algorithmic attempts to solve this problem…