In 1973, Erd\H {o} s conjectured the existence of high girth $(n, 3, 2) $-Steiner systems.
Recently, Glock, K\"{u} hn, Lo, and Osthus and independently Bohman and Warnke proved …

A Latin square is an $ n $ by $ n $ grid filled with $ n $ symbols so that each symbol appears
exactly once in each row and each column. A transversal in a Latin square is a collection of …

Rainbow matchings in graphs and in hypergraphs have been studied extensively, one
motivation coming from questions on matchings in 3‐partite hypergraphs, including …

A properly edge-colored graph is a graph with a coloring of its edges such that no vertex is
incident to two or more edges of the same color. A subgraph is called rainbow if all its edges …

We prove that every family of (not necessarily distinct) even cycles on some fixed-vertex set
has a rainbow even cycle (that is, a set of edges from distinct's, forming an even cycle). This …

Given a multi-hypergraph $ G $ that is edge-colored into color classes $ E_1,\ldots, E_n $, a
full rainbow matching is a matching of $ G $ that contains exactly one edge from each color …

This is a survey paper on rainbow sets (another name for “choice functions”). The main
theme is the distinction between two types of choice functions: those having a large (in the …

We consider the following question by Balister, Győri and Schelp: given 2n− 1 nonzero
vectors in Fn 2 with zero sum, is it always possible to partition Fn 2 into pairs such that the …

A conjecture of the first two authors is that $ n $ matchings of size $ n $ in any graph have a
rainbow matching of size $ n-1$. We prove a lower bound of $\frac {2}{3} n-1$, improving on …

Many well-known problems in combinatorics can be reduced to finding a large rainbow
structure in a certain edge-coloured multigraph. Two celebrated examples of this are …