Author

Hanzhi Bai

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Preprint Sep 2026

Sharp connectivity thresholds for mixed rigidity packings and improved bounds for highly connected orientations of graphs

Garamv\"olgyi, Jord\'an, Kir\'aly and Vill\'anyi [{{\bf Forum Math. Pi} \textbf{13} (2025), Paper No.~e11}] posed two sharp connectivity conjectures for packing rigid spanning subgraphs: one for the equal-dimensional case and the other for the packing of a $d$-rigid spanning subgraph with a spanning tree. We prove a un...

Han-Zhi Bai, Jørgen Bang-Jensen, Jin Yan · 0 citations

Preprint Aug 2026

Packing and Covering Cycles Through Prescribed Vertices

Let $G$ be a finite simple graph and let $S\subseteq V(G)$. We prove that the minimum number of vertices meeting every cycle that intersects $S$ is at most the maximum number of vertices of $S$ covered by a collection of vertex-disjoint cycles. This answers a question posed by Bowler, Ghorbani, Gut, Jacobs, and Reich [...

Han-Zhi Bai, Jin Yan · 0 citations

Preprint Aug 2026

Hitting Maximum Independent Sets in Dense and Highly Connected Graphs

For a graph $G$, let $h(G)$ be the minimum cardinality of a vertex set meeting every maximum independent set of $G$. We establish two complementary reduction principles for the Bollob\'as--Erd\H{o}s--Tuza conjecture: the conjecture for arbitrary graphs is equivalent to its restriction to regular graphs of any fixed pos...

Han-Zhi Bai, Yu-jeong Chang, Jin Yan · 0 citations