5 citations · 6 across the 20 of their papers we have counts for
11 papers · 2 filters
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…
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…
A Linearly-growing Conversion from the Set Splitting Problem to the Directed Hamiltonian Cycle Problem
Michael Haythorpe, Jerzy Filar
We consider a direct conversion of the, classical, set splitting problem to the directed Hamiltonian cycle problem. A constructive procedure for such a conversion is given, and it…
FHCP Challenge Set: The First Set of Structurally Difficult Instances of the Hamiltonian Cycle Problem
Michael Haythorpe
The FHCP Challenge Set, comprising of 1001 instances of Hamiltonian cycle problem, is introduced. This set is the first to contain instances of Hamiltonian cycle problem for which…
Constructing Arbitrarily Large Graphs with a Specified Number of Hamiltonian Cycles
Michael Haythorpe
A constructive method is provided that outputs a directed graph which is named a broken crown graph, containing vertices and Hamiltonian cycles for any choice of integer…
Linearly-growing Reductions of Karp's 21 NP-complete Problems
Jerzy A Filar, Michael Haythorpe, Richard Taylor
We address the question of whether it may be worthwhile to convert certain, now classical, NP-complete problems to one of a smaller number of kernel NP-complete problems. In partic…