기초과학연구원 이산수학그룹
On March 10, 2026, Dario Cavallaro from the TU Berlin gave a talk at the Discrete Math Seminar on well-quasi-ordering of Eulerian digraphs under (strong) immersion. The title of his talk was “Well-quasi-ordering Eulerian directed graphs by (strong) immersion“.
Directed graphs prove to be very hard to tame in contrast to undirected graphs. In particular, they are not well-quasi-ordered by any known relevant inclusion relation, and are lacking fruitful structure theorems. This motivates the search for structurally rich subclasses of directed graphs that are well behaved. Eulerian directed graphs are a particularly prominent example, sharing many similarities with undirected graphs. In fact, it is conjectured that Eulerian directed graphs are well-quasi-ordered by weak immersion, and even well-quasi-ordered by strong immersion when restricting to classes of bounded degree. We believe that we have a proof of both conjectures, and I will report on the current status, progress, and steps towards said proof and its implications. This is joint work with Ken-ichi Kawarabayashi and Stephan Kreutzer.