Splits graphs, Tyshkevich decomposition and P-stabile degree sequences
The split graphs were introduced in 1977 by Foldes and Hammer, as a mean to deal with game theoretical concepts. The notion is widely used in Combinatorics as well, especially in extremal graph theory.
In 1978 Tyshkevich observed that any graph can be uniquely decomposed into product of a series of splits graphs (and possible one simple graph). The product is associative but not commutative. (The result in English was published only in 2000.) As far as I understand there is no clear generalization (or, if you like,
narrowing) of this notion for bipartite graphs. Two years ago such notion was introduced in connection with sampling graphical realizations of bipartite degree sequences. I will talk about this connection, and some general properties of bipartite Tyshkevich product. I also will discuss some connection of the notion with P-stabile degree sequences.
About Pure mathematics seminars
We present regular seminars on a range of pure mathematics interests. Students, staff and visitors to UQ are welcome to attend, and to suggest speakers and topics.
Seminars are usually held on Tuesdays from 2 to 3pm.
Talks comprise 45 minutes of speaking time plus five minutes for questions and discussion.
Information for speakers
Researchers in all pure mathematics fields attend our seminars, so please aim your presentation at a general mathematical audience.
Contact us
To volunteer to talk or to suggest a speaker, email Ole Warnaar or Ramiro Lafuente.