Tur\'an-Type Extremal Results for Distance-$k$ Graphs
Combinatorics
2026-05-01 v1
Abstract
We study Tur\'an-type extremal problems for distance graphs, motivated by work of Csikv\'ari, Bollob\'as, Tyomkyn, and Uzzell. We determine the maximum number of vertex pairs at distance three in an -vertex graph with no triangle formed by these pairs, resolving the first case of a conjecture of Tyomkyn and Uzzell. We also determine the maximum number of vertex pairs at distance two in an -vertex graph with no triangle formed by these pairs and give a complete characterization of the extremal graphs, settling another problem of Tyomkyn and Uzzell.
Keywords
Cite
@article{arxiv.2604.28060,
title = {Tur\'an-Type Extremal Results for Distance-$k$ Graphs},
author = {Zhen He and Nika Salia and Casey Tompkins and Xiutao Zhu},
journal= {arXiv preprint arXiv:2604.28060},
year = {2026}
}