On the structure of graphs with given odd girth and large algebraic connectivity
A classical result of Andr\'asfai, Erd\H{o}s, and S\'os states that every $n$-vertex graph with odd girth at least $2k+1$ and minimum degree larger than $\frac{2n}{2k+1}$ is bipartite. Rather than imposing a minimum-degree condition, in this paper we investigate conditions on algebraic connectivity that force graphs of...