### Abstract

Let G be any graph with property P (for example, general graph, directed graph, etc.) and S be nonnegative and non-decreasing integer sequence(s). The prescribed degree sequence problem is a problem to determine whether there is a graph G having S as the prescribed sequence(s) of degrees or outdegrees of the vertices. From 1950's, P has attracted wide attentions, and its many extensions have been considered. Let P be the property satisfying the following (1) and (2): G is a directed graph with two disjoint vertex sets A and B. There are r_{11} (r_{22}, respectively) directed edges between every pair of vertices in A(B), and r_{12} directed edges between every pair of vertex in A and vertex in B. Then G is called an (r_{11}, r _{12}, r_{22}) -tournament ("tournament", for short). The problem is called the score sequence pair problem of a " tournament" (realizable, for short). S is called a score sequence pair of a "tournament" if the answer of the problem is "yes." In this paper, we propose the characterizations of a score sequence pair of a "tournament" and an algorithm for determining in linear time whether a pair of two integer sequences is realizable or not.

Original language | English |
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Pages (from-to) | 440-447 |

Number of pages | 8 |

Journal | IEICE Transactions on Information and Systems |

Volume | E90-D |

Issue number | 2 |

DOIs | |

Publication status | Published - 2007 Feb |

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### Keywords

- Algorithm
- Graph theory
- Prescribed degrees
- Score sequence
- Tournament

### ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Computer Vision and Pattern Recognition
- Electrical and Electronic Engineering
- Artificial Intelligence

### Cite this

_{11}, r

_{12}, r

_{22})-tournaments - Determination of realizability.

*IEICE Transactions on Information and Systems*,

*E90-D*(2), 440-447. https://doi.org/10.1093/ietisy/e90-d.2.440