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Treewidth versus clique number: induced minors

Claire Hilaire, Martin Milanič, Nicolas Trotignon, Djordje Vasić

Abstract

We prove that a hereditary class of graphs is $(\mathsf{tw}, ω)$-bounded if and only if the induced minors of the graphs from the class form a $(\mathsf{tw}, ω)$-bounded class.

Treewidth versus clique number: induced minors

Abstract

We prove that a hereditary class of graphs is -bounded if and only if the induced minors of the graphs from the class form a -bounded class.

Paper Structure

This paper contains 4 sections, 5 theorems, 2 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. The main result
  4. Concluding remarks

Key Result

Theorem 3.1

There exists a function $g:\mathbb{N}\to \mathbb{N}$ such that for every $k\in \mathbb{N}$, a graph $G$ has treewidth at least $g(k)$ if and only if $G$ has a subdivision of a $k \times k$ wall as a subgraph.

Theorems & Definitions (9)

  • proof
  • Theorem 3.1
  • Lemma 3.2
  • Lemma 3.3
  • proof
  • Theorem 3.4
  • proof
  • Theorem 4.1
  • proof