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Carsten Thomassen Technical University of Denmark
Graph Decomposition Wednesday, September 22, 09:00, room A703
view recording: 
Abstract:
János Barát and I made the following conjecture: For every tree T, there is a natural
number k_{T} such that every k_{T}edgeconnected graph of size divisible by E(T) has an edge
decomposition into subgraphs each isomorphic to T. The conjecture is trivial when T has at
most two edges. When we made the conjecture we could not prove it for one single tree with
three or more edges. However, we showed that the conjecture holds for the claw (the star
with three edges) provided Tutte's 3flow conjecture is true. In fact, when restricted to the
claw, our conjecture is equivalent to the weakening of Tutte's 3flow conjecture, suggested by
Jaeger, that every graph of sufficiently high (but fixed) edgeconnectivity has an orientation
such that each vertex has the same indegree and outdegree when these numbers are reduced
modulo 3.
A few years ago, I verified the conjecture for the path with four edges, and later for the
path with three edges. I have now verified the conjecture for an infinite family of trees.

Bio sketch:
Carsten Thomassen has been Professor of Mathematics at the Technical
University of Denmark since 1981. He is editorinchief of the Journal
of Graph Theory and of the Electronic Journal of Combinatorics,
and he is on the editorial boards of Discrete Mathematics, Journal of
Combinatorial Theory Ser. B, Combinatorica, and the European Journal
of Combinatorics. He is a member of the Royal Danish Academy of
Sciences and Letters.



Peter Eades University of Sydney
On the Future of Graph Drawing Friday, September 24, 16:00, room A703
view recording: 
Abstract: Was not to be revealed prematurely.

Bio sketch:
Peter Eades is Professor of Software Technologies at the University of
Sydney. His PhD work was in Combinatorial Mathematics. His interest
in graph visualization began with some consulting contracts in the
early 1980s. Since then most of his research has been inspired by
problems in Graph Visualization (despite some brief flirtations with
Data Structures, Software Engineering, and Human User Interfaces).


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