The main focus of the conference will be on Flows and MinMax equalities.

There have been recent exciting advances towards Tutte’s famous 3-, 4-, and 5-flow conjectures. Extending Thomassen’s breakthrough work, it is now known that the 3-flow conjecture (actually Jaeger’s strengthening of it) holds for 6-edge-connected graphs. The entire conjecture would follow if the 6 could be replaced by 5.

On the other hand, there are long-standing open questions in MinMax equalities involving directed cuts. The Lucchesi-Younger Theorem, a central result in Combinatorial Optimization, asserts that, in any directed graph, the maximum number of edge-disjoint directed cuts is equal to the minimum size of a transversal of directed cuts. A dual statement, that the maximum size of a set of pairwise disjoint transversals is equal to the minimum size of a directed cut, remains open after more than 30 years.

A principal goal of this conference is to stimulate further work in both these areas.

We will take this occasion to acknowledge Daniel H. Younger’s long career in mathematics. Dan arrived at Waterloo in 1967 and spent the next 40 years studying Directed Graphs and related topics. His contributions go beyond CKY parsing of context-free grammars and the Lucchesi-Younger Theorem that bear his name. His conjectures (his extension of Gallai’s Conjecture concerning disjoint directed cycles) and intellectual curiosity (substantial questions about the Appel-Haken proof of the Four Colour Theorem) have led to others making significant contributions to Graph Theory in general and Directed Graphs in particular.