18th Intl. Symp. Graph Drawing U Konstanz

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  Carsten Thomassen
Technical University of Denmark

Graph Decomposition
Wednesday, September 22, 09:00, room A703

view recording: 700 kbps stream  250 kbps stream
Abstract: János Barát and I made the following conjecture: For every tree T, there is a natural number kT such that every kT-edge-connected 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 3-flow conjecture is true. In fact, when restricted to the claw, our conjecture is equivalent to the weakening of Tutte's 3-flow conjecture, suggested by Jaeger, that every graph of sufficiently high (but fixed) edge-connectivity 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 editor-in-chief 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: 700 kbps stream  250 kbps stream
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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