A small group (2 to 6 persons) could participate in some ongoing research of a past postdoc (Zixia Song) and a current student (Christian Altomare) of Professor Robertson. This concerns the vertex-induced subgraph inclusion relation and the conjecture of S. B. Rao's about the well-partial-ordering of degree-sequences of finite graphs. A well-partial order is a well-founded partial order with no infinite antichain (set of pairwise unrelated elements). Background theory on well-partial-orders and degree sequences of graphs can be learned easily over the quarter and would give students a good idea of what modern graph theory is about. There is also a natural research strategy that would, if successful, resolve the conjecture and a real possibility that the group could contribute.

Professor Dowling will give two introductory lectures on matroids arising from matrices and graphs and discuss three possible well-partial orders in this context. There will be assigned problems for the group. Prerequesites are minimal, but mathematical maturity will be expected. Topological aspects of graph theory do not come up and are replaced by set theoretical and numerical conditions. So far as we know the Rao conjecture was first proposed at Ohio State while Professor Rao was visiting in 1981.

To sign up for this working group, enroll for 3 credits in 693 (Robertson), call number 12387-3