R. Merris, Split graphs, Europ. J. Comb. 24 (2003), 413-430. AMS Abstracts 23 (2002), 28. Math Reviews 2004b:05064.

The main topics of this article are split graphs, their degree sequences, and the place of these split partitions at the top of the partially ordered set of graphic partitions. One application is that threshold covered partitions are unigraphic. The last section of the article consists of six open problems.

Open problem 1 asks for "a general formula ... for the cardinality of the interval [alpha,beta]." Following [C. Green and D. J. Kleitman, Longest chains in the lattice of integer partitions ordered by majorization, Europ. J. Comb. 7 (1986), 1-10], LE Min Ha and PHAN Thi Ha Duong [Strict partitions and discrete dynamical systems, unpublished manuscript] use Chip Firing to compute the height of the interval.

Open problem 4, "Find an explicit generating function for the numbers of nonisomorphic (connected) split graphs with m edges and/or n vertices." was addressed by Gordon Royle. The main result of his article, [Counting set covers and split graphs, J. Integer Sequences 3 (2000), article 002.6] is a formula for the number of nonisomorphic split graphs on n vertices.