Weakly-sparse and strongly flip-flat classes of graphs are uniformly almost-wide

TL;DR

This paper explores the properties of strongly flip-flat classes of graphs, showing that weakly sparse strongly flip-flat classes are uniformly almost-wide, thus advancing the understanding of graph class structures.

Contribution

It establishes that weakly sparse strongly flip-flat classes of graphs are necessarily uniformly almost-wide, linking two important graph class concepts.

Findings

Weakly sparse strongly flip-flat classes are uniformly almost-wide.

Provides a characterization connecting flip-flatness and almost-wideness.

Advances theoretical understanding of dense graph classes.

Abstract

In this work we take a step towards characterising strongly flip-flat classes of graphs. Strong flip-flatness appears to be the analogue of uniform almost-wideness in the setting of dense classes of graphs. We prove that strongly flip-flat classes of graphs that are weakly sparse are indeed uniformly almost-wide.