Stack-number is not bounded by queue-number

TL;DR

This paper presents a family of graphs demonstrating that stack-number can be unbounded even when queue-number is bounded by 4, resolving longstanding open problems in graph theory.

Contribution

It introduces a specific family of graphs with bounded queue-number but unbounded stack-number, answering open questions from prior research.

Findings

Queue-number at most 4 for the family of graphs

Stack-number is unbounded for the same family

Resolves open problems from Heath, Leighton, Rosenberg, Blankenship, and Oporowski

Abstract

We describe a family of graphs with queue-number at most 4 but unbounded stack-number. This resolves open problems of Heath, Leighton and Rosenberg (1992) and Blankenship and Oporowski (1999).