Nonredundant 1's in Gamma-Free Matrices

This paper studies a new method for representing $\Gamma$-free matrices, which occur in characterizations of chordal bipartite and strongly chordal graphs. We show that the number of $\Gamma$-free matrices with $n$ rows and columns (and thus the number of chordal bipartite and strongly chordal graphs with $n$ vertices) is proportional to $2^\Theta(n \log^{2} n)$, and give an asymptotically space optimal method for storing these matrices.