6 papers
The typical structure of oriented graphs and digraphs with forbidden blow-up of transitive tournaments
Meili Liang, Yue Guan, Ruiling Zheng +1
For integers \(r\ge 2\), \(t\ge 1\) and a real number \(a\in(3/2,2]\), we study the typical structure of oriented graphs and digraphs that do not contain a blow-up \(T_{r+1}^t\) of…
The typical structure of oriented graphs and digraphs with forbidden blow-up of transitive tournaments
Jianxi Liu
We study the typical structure of oriented graphs and digraphs that do not contain a blow-up T_{r+1}^t of a transitive tournament. For any integers r >= 2, t >= 1 and any real a in…
Almost all -free oriented graphs have backwards edges
Jianxi Liu, Meili Liang
We prove a conjecture of Kühn, Osthus, Townsend and Zhao \cite{kuhn2017structure} stating that almost every -free oriented graph on vertices has backwards edges in…
A container theorem for general digraphs with forbidden subdigraphs
Meili Liang, Yue Guan, Ruiling Zheng +1
In a seminal work, Kühn, Osthus, Townsend, and Zhao used the hypergraph container method to determine the typical structure of oriented graphs and digraphs avoiding a fixed tournam…
Typical structure of oriented graphs and digraphs with forbidden blow-up transitive triangle
Jianxi Liu
In this work, we establish an analogue result of the Erdös-Stone theorem of weighted digraphs using Regularity Lemma of digraphs. We give a stability result of oriented graphs and…
Note for Nikiforov's two conjectures on the energy of trees
Xueliang Li, Jianxi Liu
The energy of a graph is defined to be the sum of the absolute values of its eigenvalues. Nikiforov in {\it ``V. Nikiforov, The energy of -free graphs of bounded degree, L…