Fakulta matematiky, fyziky
a informatiky
Univerzity Komenského v Bratislave

Seminár z algebratickej teórie grafov - Robert Jajcay (6.4.2018)

v piatok 6.4.2018 o 13:30 hod. v miestnosti M 213

05. 04. 2018 10.15 hod.
Od: Martin Mačaj

Prednášajúci: Róbert Jajcay

Názov: Genus polynomials of graphs

Termín: 6.4.2018, 13:30 hod., M/213

The n-th coefficient of the genus polynomial of a graph represents the number of combinatorially non-equivalent embeddings of the graph into the surface of genus n. As usual (but still surprising) with this type of algebraic representations, viewing this entirely combinatorial object algebraically allows us to apply algebraic methods to determine the coefficients (and thus the number of embeddings). In particular, we discuss the use of the Cayley-Hamilton theorem and exhibit a surprising connection to an old enumeration result, which shows that the presented enumeration method has a wide range of applications.