On Erdős-Gallai and Havel-Hakimi algorithms

Abstract: Havel in 1955, Erd\H{o}s and Gallai in 1960, Hakimi in 1962, Ruskey, Cohen, Eades and Scott in 1994, Barnes and Savage in 1997, Kohnert in 2004, Tripathi, Venugopalan and West in 2010 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 $\Omega(n^2)$ in worst case. In this paper we propose a new algorithm called EGL (Erd\H{o}s-Gallai Linear algorithm), whose worst running time is $\Theta(n).$ As an application of this quick algorithm we computed the number of the different degree sequences of simple graphs for $24, ...,29$ vertices.