3 citations · 4 across the 10 of their papers we have counts for
13 papers
Simplifications to Guide Monte Carlo Tree Search in Combinatorial Games
Michael Haythorpe, Alex Newcombe, Damian O'Dea
We examine a type of modified Monte Carlo Tree Search (MCTS) for strategising in combinatorial games. The modifications are derived by analysing simplified strategies and simplifie…
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…
A Cross Entropy Approach to the Domination Problem and its Variants
Ryan Burdett, Michael Haythorpe, Alex Newcombe
The domination problem and several of its variants (total domination, 2-domination and secure domination) are considered. These problems have various real-world applications, but a…
Constructing Families of Cospectral Regular Graphs
Michael Haythorpe, Alex Newcombe
A set of graphs are called cospectral if their adjacency matrices have the same characteristic polynomial. In this paper we introduce a simple method for constructing infinite fami…
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…
The Secure Domination Number of Cartesian Products of Small Graphs with Paths and Cycles
Michael Haythorpe, Alex Newcombe
The secure domination numbers of the Cartesian products of two small graphs with paths or cycles is determined, as well as for Mobius ladder graphs. Prior to this work, in all case…
The maximum crossing number of
Michael Haythorpe, Alex Newcombe
We determine that the maximum crossing number of is 78, which closes the previously best known range of between 68 and 80. The proof uses several techniques which…
On the Crossing Number of the Cartesian Product of a Sunlet Graph and a Star Graph
Michael Haythorpe, Alex Newcombe
The exact crossing number is only known for a small number of families of graphs. Many of the families for which crossing numbers have been determined correspond to cartesian produ…
On the Crossing Numbers of Cartesian Products of Small Graphs with Paths, Cycles and Stars
Kieran Clancy, Michael Haythorpe, Alex Newcombe
There has been significant research dedicated towards computing the crossing numbers of families of graphs resulting from the Cartesian products of small graphs with arbitrarily la…
A survey of graphs with known or bounded crossing numbers
Kieran Clancy, Michael Haythorpe, Alex Newcombe
We present, to the best of the authors' knowledge, all known results for the (planar) crossing numbers of specific graphs and graph families. The results are separated into various…
There are no Cubic Graphs on 26 Vertices with Crossing Number 10 or 11
Kieran Clancy, Michael Haythorpe, Alex Newcombe +1
We show that no cubic graphs of order 26 have crossing number larger than 9, which proves a conjecture of Ed Pegg Jr and Geoffrey Exoo that the smallest cubic graphs with crossing…
An effective crossing minimisation heuristic based on star insertion
Kieran Clancy, Michael Haythorpe, Alex Newcombe
We present a new heuristic method for minimising crossings in a graph. The method is based upon repeatedly solving the so-called {\em star insertion problem} in the setting where t…