5 papers
Colored Turán densities and finite directed templates
Nannan Chen, Ander Lamaison, Heng Li +1
Classical Turán theory relates the asymptotic extremal problem for an ordinary forbidden graph to its chromatic number. This principle fails when a forbidden copy must respect pres…
Triple systems with bounded matching number: some constructions and exact Turán number
Nannan Chen, Miao Liu, Yuzhen Qi +1
We study the Turán numbers of -graphs avoiding -graphs and , a matching of size . We disprove a conjecture of Gerbner, Tompkins, and Zhou [European Journa…
Large cliques in graphs with forbidden semi-induced structures
Nannan Chen, Yulai Ma, Fan Yang
In 2022, Holmsen showed that any graph with at least \( c \binom{n}{r} \) \(r\)-cliques but no induced complete -partite graph must contain a clique of order \…
Exact Turán densities in triple systems
Nannan Chen, Yuzhen Qi, Caihong Yang +1
In this paper, we prove several new Turán density results for -graphs. We show: , ,…
Tiling in dense graphs
Nannan Chen, Xizhi Liu, Lin Sun +1
We determine asymptotically the two extremal constructions for the tiling problem of the -shaped tree. In particular, the first extremal construction is close to the complement…