Large cliques in graphs with forbidden semi-induced structures
Combinatorics
2025-11-18 v1
Abstract
In 2022, Holmsen showed that any graph with at least -cliques but no induced complete -partite graph must contain a clique of order . In this paper, we study graphs forbidding semi-induced substructures and show that every -vertex graph containing at least copies of (for some constant ) and forbidding semi-induced substructures, related to , must contain a clique of order . Our result strengthens Holmsen's bound by improving the dependence on from to linear in with bounded number of forbidden structures. Furthermore, our approach is naturally linked to the notion of VC-dimension.
Keywords
Cite
@article{arxiv.2511.13073,
title = {Large cliques in graphs with forbidden semi-induced structures},
author = {Nannan Chen and Yulai Ma and Fan Yang},
journal= {arXiv preprint arXiv:2511.13073},
year = {2025}
}