Hopf algebras and factorial divergent power series: Algebraic tools for graphical
enumeration
Abstract.
In quantum field theory the number of primitive graphs, which are
essentially multigraphs of higher edge-connectivity, is of special
interest. The Connes-Kreimer Hopf algebra of graphs and the ring of
factorially divergent power series can be used to extract complete
asymptotic expansions for these graph classes. I will introduce both
algebraic structures and give the complete asymptotic expansion of
cyclically 4-edge-connected cubic graphs as an example. If time
permits, I will briefly illustrate how these algebraic properties can
be generalized to broader classes of graphs.