Atlantic Graph Theory Seminar: Ferenc Bencs (University of Amsterdam)

In this talk, I will show regions that contain no complex zeros the edge-cover polynomials of hypergraphs. The edge cover polynomial of a graph $G$ is the generating function of edges that covers $V(G)$. It is known that the zeros of this polynomial have length at most $\frac{(2+\sqrt{3})^2}{1+\sqrt{3}}$, that we strengthen by showing that it is at most $4$.  We use the general subgraph counting polynomial of Wagner to establish this result along with its generalization for the edge cover polynomial of hypergraphs. As another example, we will establish a new bound on the length of the zeros of the domination and total domination polynomials of graphs in terms of the maximum degree.

Joint work with P\’eter Csikv\’ari and  Guus Regts.