The linear Tur\'an number of the 3-graph $P_5$
Combinatorics
2026-01-28 v1
Abstract
We prove that for any linear 3-graph on vertices without a path of length 5, the number of edges is at most , and the equality holds if and only if the graph is the disjoint union of , a graph with 11 vertices and 15 edges. Thus, , and the equality holds if and only if .
Cite
@article{arxiv.2601.19068,
title = {The linear Tur\'an number of the 3-graph $P_5$},
author = {Chaoliang Tang and Hehui Wu and Junchi Zhang},
journal= {arXiv preprint arXiv:2601.19068},
year = {2026}
}