6 papers
Sharp connectivity thresholds for mixed rigidity packings and improved bounds for highly connected orientations of graphs
Hanzhi Bai, Jørgen Bang-Jensen, Jin Yan
Garamvölgyi, Jordán, Király and Villányi [{{\bf Forum Math. Pi} \textbf{13} (2025), Paper No.~e11}] posed two sharp connectivity conjectures for packing rigid spanning subgraphs: o…
Hitting Maximum Independent Sets in Dense and Highly Connected Graphs
Hanzhi Bai, Yufei Chang, Jin Yan
For a graph , let be the minimum cardinality of a vertex set meeting every maximum independent set of . We establish two complementary reduction principles for the Bol…
Paths with Prescribed Endpoints in Semicomplete and Locally Semicomplete Digraphs
Hanzhi Bai, Jin Yan, Jia Zhou
We study two open path problems with prescribed endpoints posed by Bang-Jensen and Gutin. The first asks for a longest -path in a semicomplete digraph. The second asks wheth…
Packing and Covering Cycles Through Prescribed Vertices
Hanzhi Bai, Jin Yan
Let be a finite simple graph and let . We prove that the minimum number of vertices meeting every cycle that intersects is at most the maximum number of ve…
Polynomial Algorithms for Minimum Degree Partitions in Semicomplete Digraphs
Hanzhi Bai, Jin Yan
A 2-partition of a digraph is a partition of its vertex set into two nonempty parts. Degree-constrained 2-partition problems are generally computationally difficult, even when the…
New Tower-Type Lower Bounds for Hypergraph Ramsey Numbers
Hanzhi Bai, Longma Du, Xinyu Hu +2
The Ramsey number is the smallest such that any red/blue coloring of the -subsets of contains a red -set or a blue -set. For fixed and , and fo…