Algebraic structures based on graph contraction

In this talk, I will introduce a new algebraic structure called "contractad" resembling the contraction of a subgraph in a simple connected graph.

Examples of contractads include Hamiltonian paths, spanning trees, and configuration spaces.

These examples admit presentations with quadratic relations and standard methods of homological algebra may help us to get functional equations for generating series.

As an application, I will show a simple generating series counting Hamilton paths, Hamilton cycles and chromatic polynomials for complete multipartite graphs.

The talk is based on joint works with D.Lyskov.