### Marco Colombo (University of Edinburgh)

#### A branch-and-cut approach to solve the Hamiltonian cycle problem

*Wednesday 10 March 2004 at 15.30, JCMB 6206*

##### Abstract

The Hamiltonian Cycle Problem (HCP) is the problem to find a cycle in a
graph such that all vertices are visited exactly once. This problem is
easily stated, but unfortunately it's an extremely difficult integer
programming problem.

In this talk I will present a nonconvex quadratic formulation of the HCP,
together with the Branch-and-Cut framework that guides the interior-point
solver towards an integer solution.

A preliminary implementation exists, and numerical results are given for
different types of cutting planes. The results suggest that the nonconvex
quadratic formulation outperforms a linear formulation for large scale
problems.

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