Scott's induced subdivision conjecture for maximal triangle-free graphs

TL;DR

This paper verifies Scott's conjecture that graphs with no induced subdivision of a fixed graph are -bounded, specifically confirming it for the class of maximal triangle-free graphs, thus advancing understanding of graph coloring constraints.

Contribution

The paper proves Scott's induced subdivision conjecture for the specific case of maximal triangle-free graphs, a previously unresolved case.

Findings

Confirmed Scott's conjecture for maximal triangle-free graphs

Established -boundedness for this class of graphs

Enhanced understanding of induced subdivision constraints in graph theory

Abstract

Scott conjectured that the class of graphs with no induced subdivision of a given graph is $\chi$-bounded. We verify his conjecture for maximal triangle-free graphs.