Hard Problems That Quickly Become Very Easy

TL;DR

This paper demonstrates that certain computationally hard problems become trivial when restricted to specific hereditary graph classes, highlighting the impact of graph class restrictions on problem complexity.

Contribution

It provides examples of NP-hard, PSPACE-complete, and NEXPTIME-complete problems that are constant-time solvable on all hereditary graph classes except the class of all graphs.

Findings

Hard problems become trivial on hereditary graph classes

Examples include NP-hard, PSPACE-complete, NEXPTIME-complete problems

Complexity drastically reduces under hereditary restrictions

Abstract

A graph class is hereditary if it is closed under vertex deletion. We give examples of NP-hard, PSPACE-complete and NEXPTIME-complete problems that become constant-time solvable for every hereditary graph class that is not equal to the class of all graphs.