They are chordal.

A split graph is an undirected graph whose vertices can be partitioned into two sets such that one set induces a complete subgraph and the other set has no edges between vertices.

The complement of a split graph is a split graph.

A graph is a split graph if and only if it
is chordal and has a chordal complement.^{1}

- Future editions will include a proof. ↩︎