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

Pages | 1019-1022 |

Number of pages | 4 |

DOIs | |

Publication status | Published - 2006 |

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

### Other

Other | APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems |
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Period | 06/12/4 → 06/12/6 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

_{11}, r

_{12}, r

_{22})-tournament. In

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

**Realizability of Score sequence pair of an (r _{11}, r_{12}, r_{22})-tournament.** / Takahashi, Masaya; Watanabe, Takahiro; Yoshimura, Takeshi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

_{11}, r

_{12}, r

_{22})-tournament. in

*IEEE Asia-Pacific Conference on Circuits and Systems, Proceedings, APCCAS.*, 4145569, pp. 1019-1022, APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems, 06/12/4. https://doi.org/10.1109/APCCAS.2006.342261

_{11}, r

_{12}, r

_{22})-tournament. In IEEE Asia-Pacific Conference on Circuits and Systems, Proceedings, APCCAS. 2006. p. 1019-1022. 4145569 https://doi.org/10.1109/APCCAS.2006.342261

}

TY - GEN

T1 - Realizability of Score sequence pair of an (r11, r12, r22)-tournament

AU - Takahashi, Masaya

AU - Watanabe, Takahiro

AU - Yoshimura, Takeshi

PY - 2006

Y1 - 2006

N2 - 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}|= {r11 if u, v∈ A {r 12 if u∈ A, v∈ B {r22 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 (r11,r12,r22)-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.

AB - 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}|= {r11 if u, v∈ A {r 12 if u∈ A, v∈ B {r22 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 (r11,r12,r22)-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.

KW - Algorithm

KW - Graph theory

KW - Prescribed degrees

KW - Realizable

KW - Score sequence

KW - Tournament

UR - http://www.scopus.com/inward/record.url?scp=50249089565&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=50249089565&partnerID=8YFLogxK

U2 - 10.1109/APCCAS.2006.342261

DO - 10.1109/APCCAS.2006.342261

M3 - Conference contribution

AN - SCOPUS:50249089565

SN - 1424403871

SN - 9781424403875

SP - 1019

EP - 1022

BT - IEEE Asia-Pacific Conference on Circuits and Systems, Proceedings, APCCAS

ER -