Motivated by the exact weight perfect matching problem and recent parameterized algorithms for finding an $\ell$-th smallest perfect matching, in the paper A hierarchy of edge-weight symmetries in perfect matchings we study structural properties of edge-weight symmetries in graphs. Recent work by El Maalouly et al. (ESA 2025) showed that excluding all perfect matchings whose…
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 colors. Since finding such a tree is NP-hard in general, previous work often relied on minimum color degree conditions to guarantee the existence of…
The year kicked off in the same great way the last one finished: our research group’s paper on $\{s,t\}$-separating principal partition sequences has been accepted to IPCO 2026!
The end of 2025 has been very successful for the research group in terms of publications: several of our submitted papers have been accepted by leading journals, including JCTB, Combinatorica, and SIDMA. It has been a challenging period with a lot of hard work, but we are happy to share the good news that, thanks…
The multiple exchange property for matroid bases states that for any bases $A$ and $B$ of a matroid and any subset $X\subseteq A\setminus B$, there exists a subset $Y\subseteq B\setminus A$ such that both $A-X+Y$ and $B+X-Y$ are bases. This classical result has not only found applications in matroid theory, but also in the analysis…