## Abstract

Given a degree sequence d of length n, the degree realization problem is to decide if d has a realization. That is a n-vertex graph whose degree sequence is d, and if this is the case, to construct such a realization (cf. [6, 7, 8]). We consider the following natural generalization of the problem: Let G = (V,E) be a simple undirected graph on V = {1, 2, . . . , n}. Let f 2 Nn be a vector of vertex-requirements, and let w 2 Nn be a vector of vertex-weights. The weight vector w satisfies the requirement vector f on G if the constraints P j2..(i) wj = fi are satisfied for all i 2 V , where ..(i) denotes the neighborhood of i. The vertex-weighted realization problem is now as follows: Given a requirements vector f, find a suitable graph G and a weight vector w that satisfy f on G. In the original degree realization problem, all vertex weights are equal to one.

Original language | English |
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Pages | 9-12 |

Number of pages | 4 |

State | Published - 2019 |

Event | 17th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW 2019 - Enschede, Netherlands Duration: 1 Jul 2019 → 3 Jul 2019 |

### Conference

Conference | 17th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW 2019 |
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Country/Territory | Netherlands |

City | Enschede |

Period | 1/07/19 → 3/07/19 |

### Bibliographical note

Publisher Copyright:© Proceedings of the 17th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW 2019.