On Erdős-Gallai and Havel-Hakimi algorithms

Havel in 1955 [28], Erdős and Gallai in 1960 [21], Hakimi in 1962 [26], Ruskey, Cohen, Eades and Scott in 1994 [69], Barnes and Savage in 1997 [6], Kohnert in 2004 [49], Tripathi, Venugopalan and West in 2010 [83] proposed a method to decide, whether a sequence of nonnegative integers can be the degree sequence of a simple graph. The running time of their algorithms is Ω(n) in worst case. In this paper we propose a new algorithm called EGL (Erdős-Gallai Linear algorithm), whose worst running time is Θ(n). As an application of this quick algorithm we computed the number of the different degree sequences of simple graphs for 24, . . . , 29 vertices (see [74]).