FHCP Challenge Set: The First Set of Structurally Difficult Instances of the Hamiltonian Cycle Problem

TL;DR

The FHCP Challenge Set introduces 1001 structurally challenging Hamiltonian cycle problem instances, emphasizing graph structure over size, and reports on a year-long competition to solve them.

Contribution

This work presents the first set of Hamiltonian cycle instances where difficulty stems from graph structure, along with a comprehensive challenge and competition results.

Findings

First set of structurally difficult Hamiltonian cycle instances

Successful completion of a year-long challenge to solve all instances

Insights into graph structures that increase problem difficulty

Abstract

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 the primary difficulty is the underlying graph structure, rather than simply size. A summary of the kinds of graphs contained in the FHCP Challenge Set is given. A discussion of the results of the FHCP Challenge, a year-long competition to solve all instances of the FHCP Challenge Set first announced at the 59th Annual Meeting for the Australian Mathematical Society, is also included.