# The Generalized Dehn Property

## TL;DR

This paper investigates a generalized Dehn property allowing cutcells, providing counterexamples that challenge the conjecture that it implies a linear isoperimetric inequality.

## Contribution

It introduces counterexamples to the conjecture that the generalized Dehn property with cutcells still guarantees a linear isoperimetric inequality.

## Key findings

- Counterexamples disprove the conjecture.
- The generalized Dehn property does not necessarily imply linear isoperimetric inequality.

## Abstract

The Dehn property for a complex is that every non-trivial disk diagram has spurs or shells. It implies a linear isoperimetric inequality. It has been conjectured that the same is true of a more general property which also allows cutcells. We give counterexamples. La propri\'et\'e Dehn pour un complexe est que chaque diagramme de disque non trivial a des \'eperons ou des shells. Cela implique une in\'egalit\'e isop\'erim\'etrique lin\'eaire. Il a \'et\'e suppos\'e qu'il en \'etait de m\^eme pour une propri\'et\'e plus g\'en\'erale qui autorise \'egalement les cellules de coupe. Nous pr\'esentons des contre-exemples.