Split graphs

This chapter provides an introduction to split graphs and related classes, presenting both classical results and recent advances. Degree sequences play a crucial role, and we study these geometrically using Ferrers diagrams in Section 4, and as the basis for three-part partitions in Section 5. Bijections between graph classes and a formula for counting the number of unlabelled split graphs on n vertices allow us to count additional classes of graphs related to split graphs. We conclude by presenting a graph decomposition theorem in which split graphs play a starring role.