### Abstract

Let G be any directed graph 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 with S as the prescribed sequence(s) of outdegrees of the vertices. Let G be the property satisfying the following (1) and (2): (1) G has two disjoint vertex sets A and B. (2) For every vertex pair u, v∈ G (u ≠ v), G satisfies |{HV}| + |{VH}|= {r_{11} if u, v∈ A {r _{12} if u∈ A, v∈ B {r_{22} if u, v ∈ B, where uv (vu, respectively) means a directed edges from u to v (from v to u). Then G is called an (r_{11},r_{12},r_{22})-tournament ("tournament", for short). When G is a "tournament," the prescribed degree sequence problem is called the score sequence pair problem of a "tournament", and S is called a score sequence pair of a "tournament" (or S is realizable) if the answer is "yes." In this paper, we propose the characterizations 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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Title of host publication | APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems |

Pages | 1019-1022 |

Number of pages | 4 |

DOIs | |

Publication status | Published - 2006 Dec 1 |

Event | APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems - , Singapore Duration: 2006 Dec 4 → 2006 Dec 6 |

### Publication series

Name | IEEE Asia-Pacific Conference on Circuits and Systems, Proceedings, APCCAS |
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### Conference

Conference | APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems |
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Country | Singapore |

Period | 06/12/4 → 06/12/6 |

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### Keywords

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

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

_{11}, r

_{12}, r

_{22})-tournament. In

*APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems*(pp. 1019-1022). [4145569] (IEEE Asia-Pacific Conference on Circuits and Systems, Proceedings, APCCAS). https://doi.org/10.1109/APCCAS.2006.342261