The Combinatorics, Probability and Algorithms seminar is usually held weekly during termtime.
Thursday 2 October 2025, 13:00-14:00
Watson Building, B16
Given a poset $P$, a family $\mathcal F$ of points in the Boolean lattice is said to be induced-$P$-saturated if (1) $\mathcal F$ contains no copy of $P$ as an induced (i.e., strong) subposet and (2) every strict superset of $\mathcal F$ contains a copy of $P$ as an induced subposet. The minimum size of an induced-$P$-saturated family in the Boolean lattice of dimension $n$ is denoted by $\mathrm{sat}^*(n,P)$.
The notion was introduced by Ferrara, Kay, Kramer, Martin, Reiniger, Smith, and Sullivan (2017) based in part on a previous notion of not-necessarily-induced saturation by Gerbner, Keszegh, Lemons, Palmer, Pálvölgyi, and Patkós (2013), which parallels the deep literature on the saturation function for graphs. Although induced saturation in graphs is not a natural concept, it seems to be particularly natural in the setting of posets.
In this talk, we discuss the classical results and new developments on bounds of $\mathrm{sat}^*(n,P)$ for well-studied posets $P$.
Thursday 9 October 2025, 14:00-15:00
Watson Building, B16
Given an integer $k \ge 1$, an edge-$k$-colouring of a graph $G$ is an assignment of colours $1, \dots, k$ to the edges of $G$ such that no two adjacent edges receive the same colour. A vertex-distinguishing (resp. sum-distinguishing) edge-$k$-colouring of $G$ is an edge-$k$-colouring in which, for every pair of distinct vertices $u$ and $v$, the set (resp. the sum) of colours assigned to the edges incident with $u$ differs from that assigned to the edges incident with $v$.
The vertex-distinguishing chromatic index (resp. sum-distinguishing chromatic index), denoted by $\chi'_{vd}(G)$ (resp. $\chi'_{sd}(G)$), is the minimum integer $k$ such that $G$ admits a vertex-distinguishing (resp. sum-distinguishing) edge-$k$-colouring.
In this talk, we will present some recent progress on vertex-distinguishing and sum-distinguishing edge-colourings of graphs. This work is joint with Songling Shan, Guanghui Wang, and Yiming Zhou.
Thursday 16 October 2025, 13:00-14:00
Watson Building, B16
An $H$-packing in a graph $G$ is a collection of vertex-disjoint copies of $H$. We show that for every constant $c > 0$ and bipartite graph $H$, every $d$-regular $n$-vertex graph with $d > cn$ has an $H$-packing covering all but a constant number of vertices. This resolves a problem by Kühn and Osthus from 2015, and is a joint work with Abhishek Methuku and Benny Sudakov.
Thursday 23 October 2025, 13:00-14:00
Watson Building, B16
Abstract: TBA
Thursday 30 October 2025, 13:00-14:00
Watson Building, B16
Abstract: TBA
Thursday 6 November 2025, 13:00-14:00
Watson Building, B16
Abstract: TBA
Thursday 13 November 2025, 13:00-14:00
Watson Building, B16
Abstract: TBA
Thursday 20 November 2025, 13:00-14:00
Watson Building, B16
Abstract: TBA
Thursday 27 November 2025, 13:00-14:00
Watson Building, B16
Abstract: TBA
Thursday 4 December 2025, 13:00-14:00
Watson Building, B16
Abstract: TBA