### 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 |{uv}| + |{vu}| = [ r_{11} if u, v ∈ A r _{12} if u, v∈ 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." We proposed the characterizations of a "tournament" and an algorithm for determining in linear time whether a pair of two integer sequences is realizable or not [5]. In this paper, we propose an algorithm for constructing a "tournament" from such a score sequence pair.

Original language | English |
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Article number | 4253410 |

Pages (from-to) | 3403-3406 |

Number of pages | 4 |

Journal | Proceedings - IEEE International Symposium on Circuits and Systems |

Publication status | Published - 2007 Sep 27 |

Event | 2007 IEEE International Symposium on Circuits and Systems, ISCAS 2007 - New Orleans, LA, United States Duration: 2007 May 27 → 2007 May 30 |

### Keywords

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

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

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## Cite this

_{11}, r

_{12}, r

_{22})- tournament from a score sequence pair.

*Proceedings - IEEE International Symposium on Circuits and Systems*, 3403-3406. [4253410].