Unavoidable vertex-minors in large prime graphs

2013/10/04 Friday 4PM-5PM

ROOM 1409

ROOM 1409

A split of a graph is a partition

*(A,B)*of the vertex set*V(G)*having subsets*A*_{0}of*A*and*B*_{0}of*B*such that |*A*|,|*B*| > 1 and a vertex*a*in*A*is adjacent to a vertex*b*in*B*if and only if a is in*A*_{0}and*b*is in*B*_{0}. A graph is prime (with respect to the split decomposition) if it has no split.We prove that for each *n*, there exists *N* such that every prime graph on at least *N* vertices contains a vertex-minor isomorphic to either a cycle of length *n* or a graph consisting of two disjoint cliques of size *n* joined by a matching.

In this talk, we plan to describe a main tool, which is called a blocking sequence in a prime graph, and we will describe two big steps of the proof. And we will pose some open problems behind this result.

This is a joint work with Sang-il Oum.

Tags: 권오정