Clique immersions and independence number

Sebastián Bustamante, Daniel A. Quiroz, Maya Stein, José Zamora

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

The analogue of Hadwiger's conjecture for the immersion order states that every graph G contains Kχ(G) as an immersion. If true, this would imply that every graph with n vertices and independence number α contains K⌈[Formula presented]⌉ as an immersion. The best currently known bound for this conjecture is due to Gauthier, Le and Wollan, who recently proved that every graph G contains an immersion of a clique on ⌈[Formula presented]⌉ vertices. Their result implies that every n-vertex graph with independence number α contains an immersion of a clique on ⌈[Formula presented]−1.13⌉ vertices. We improve on this result for all α≥3, by showing that every n-vertex graph with independence number α≥3 contains an immersion of a clique on ⌊[Formula presented]⌋−1 vertices, where f is a nonnegative function.

Original languageEnglish
Article number103550
JournalEuropean Journal of Combinatorics
Volume106
DOIs
Publication statusPublished - Dec 2022

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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