(This working group is continuing from the winter quarter, and participation in the winter quarter, or permission of the instructor, is a prerequisite.)

We will study the connection between finite graph symmetry and cyclic accessibility.

Following a problem of Lovasz in 1969 it is believed that every finite connected graph, G, that is vertex transitive (Aut(G) acts transitively on the vertices of G) has a Hamilton path (a simple path passing thru every vertex). A special case of this conjecture is for Cayley graphs of finite group presentations with more than two elements. This has been shown to be true for presentations of the form <a,b | a2=b^s=(ab)3=1, etc.>. We will work on the generalization to <a,b | a2=b^s=(ab)4=1, etc.>. This is the next step in proving that the Cayley graph of every finite group presentation has a Hamilton path. This in turn is the next step to showing that every finite group presentation is Hamiltonian (has a Hamilton cycle). A pdf file for the <2,s,3> result is a MRI report and is posted on the MRI website.

To sign up for this working group, enroll for 3 credits in 693 (Glover), call number 12347-1

For more information, contact Henry Glover (glover@math.ohio-state.edu)