5 papers
The Complexity of Weak Saturation for Complete Graphs and Balanced Complete Bipartite Graphs
Yihan Chen, Tianying Xie
For graphs and , a spanning subgraph of is weakly -saturated in if the edges in can be added one at a time, each addition creating a new…
Two problems of Burr, Erd\H os, Graham, and Sós on maximal anti-Ramsey functions for
Mingze Li, Bo Ning, Tianying Xie
Burr, Erd\H os, Graham, and Sós introduced the maximal anti-Ramsey function , the minimum number of colors required over all -vertex graphs with at least…
Saturation numbers for -uniform Berge-
Yihan Chen, Jialin He, Tianying Xie
The saturation number is the minimum number of hyperedges in an -uniform -saturated hypergraph on vertices. We determine this para…
Planar Turán number of quasi-double stars
Huiqing Liu, Tian Xie, Qin Zhao
Given a graph H, we call a graph if it does not contain H as a subgraph. The planar Turán number of a graph H, denoted by , is the maximum…
On the -clique cover number of graphs
Yihan Chen, Jialin He, Tianying Xie
In 1966, Erdős, Goodman, and Pósa proved that cliques are sufficient to cover all edges in any -vertex graph, with tightness achieved by the balanced com…