기초과학연구원 이산수학그룹
On September 9, 2025, Katherine Perry from the Soka University of America gave a talk at the Discrete Math Seminar on the relationship between the distinguishing number and the fixing number of trees. The title of her talk was “Symmetry breaking in trees“.
We will discuss two symmetry breaking parameters: distinguishing number and fixing number. Despite being introduced independently, they share meaningful connections. In particular, we show that if a tree is 2-distinguishable with order at least 3, it suffices to fix at most 4/11 of the vertices and if a tree is $d$-distinguishable, $d \geq 3$, it suffices to fix at most $\frac{d-1}{d+1}$ of the vertices. We also characterize the $d$-distinguishable trees with radius $r$, for any $d \geq 2$ and $r \geq 1$.
This is joint work with Calum Buchanan, Peter Dankleman, Isabel Harris, Paul Horn, and Emily Rivett-Carnac.