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math.CO2026
Joins and ear decompositions beyond graphic matroids
Yuhang Bai, Kristóf Bérczi, Chaitanya Nalam
For a matroid , a join is a set that meets every circuit in at most elements. Let denote the maximum size of a join. Motivated by Frank's mi…
cs.DS2026
Above-Guarantee Algorithm for Properly Colored Trees
Yuhang Bai, Kristóf Bérczi
In the Properly Colored Spanning Tree problem, we are given an edge-colored undirected graph and the goal is to find a spanning tree in which any two adjacent edges have distinct c…
math.CO2026
Most probably trangle-free graphs
Yuhang Bai, Gyula O. H. Katona, Zixuan Yang
The celebrated Mantel's theorem states that any triangle-free graph on vertices contains at most edges. It is natural to ask how many triangle…