### Abstract

One of the simplest ways to decide whether a given finite sequence of positive integers can arise as the degree sequence of a simple graph is the greedy algorithm of Havel and Hakimi. This note extends their approach to directed graphs. It also studies cases of some simple forbidden edge-sets. Finally, it proves a result which is useful to design an MCMC algorithm to find random realizations of prescribed directed degree sequences.

Original language | English |
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Pages (from-to) | 1-10 |

Number of pages | 10 |

Journal | Electronic Journal of Combinatorics |

Volume | 17 |

Issue number | 1 |

Publication status | Published - Aug 20 2010 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics

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## Cite this

Erdos, P. L., Miklós, I., & Toroczkai, Z. (2010). A simple havel hakimi type algorithm to realize graphical degree sequences of directed graphs.

*Electronic Journal of Combinatorics*,*17*(1), 1-10.