3 papers
math.CO2026
New bounds for proper -conflict-free colourings
Quentin Chuet, Tianjiao Dai, Qiancheng Ouyang +1
A proper -colouring of a graph is called -conflict-free if every vertex has at least colours appearing exactly once in its neighbourhood.…
math.CO2025
An exact Ore-degree condition for Hamilton cycles in oriented graphs
Yulin Chang, Yangyang Cheng, Tianjiao Dai +2
An oriented graph is a digraph that contains no 2-cycles, i.e., there is at most one arc between any two vertices. We show that every oriented graph of sufficiently large order…
math.CO2025
Independent transversal blow-up of graphs
Tianjiao Dai, Weichan Liu, Xin Zhang
In an -partite graph, an independent transversal of size (ITS) consists of vertices from each part forming an independent set. Motivated by a question from Bollobás, Er…