# Seminars & Events for Discrete Mathematics Seminar

##### Stability results in graphs of given circumference

In this talk we will discuss some Turan-type results on graphs with a given circumference. Let W_{n,k,c} be the graph obtained from a clique K_{c-k+1} by adding n-(c-k+1) isolated vertices each joined to the same k vertices of the clique, and let f(n,k,c)=e(W_{n,k,c}). Improving the Erdos-Gallai theorem, Kopylov proved in 1977 that for c<n, any 2-connected graph G on n vertices with circumference c has at most max (f(n,2,c),f(n,[c/2],c)) edges, with equality if and only if G equals W_{n,2,c} or W_{n,[c/2],c}. Recently, Furedi et al. obtained a stability version of Kopylov's theorem.