### 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 |
---|---|

Title of host publication | Proceedings - IEEE International Symposium on Circuits and Systems |

Pages | 3403-3406 |

Number of pages | 4 |

Publication status | Published - 2007 |

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

### Other

Other | 2007 IEEE International Symposium on Circuits and Systems, ISCAS 2007 |
---|---|

Country | United States |

City | New Orleans, LA |

Period | 07/5/27 → 07/5/30 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Electrical and Electronic Engineering

### Cite this

_{11}, r

_{12}, r

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

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

**Construction of an (r
_{11}, r
_{12}, r
_{22})- tournament from a score sequence pair
.** / Takahashi, Masaya; Watanabe, Takahiro; Yoshimura, Takeshi.

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

_{11}, r

_{12}, r

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

*Proceedings - IEEE International Symposium on Circuits and Systems.*, 4253410, pp. 3403-3406, 2007 IEEE International Symposium on Circuits and Systems, ISCAS 2007, New Orleans, LA, United States, 07/5/27.

_{11}, r

_{12}, r

_{22})- tournament from a score sequence pair In Proceedings - IEEE International Symposium on Circuits and Systems. 2007. p. 3403-3406. 4253410

}

TY - GEN

T1 - Construction of an (r 11, r 12, r 22)- tournament from a score sequence pair

AU - Takahashi, Masaya

AU - Watanabe, Takahiro

AU - Yoshimura, Takeshi

PY - 2007

Y1 - 2007

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 |{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.

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 |{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.

KW - Algorithm

KW - Construction

KW - Graph theory

KW - Prescribed degrees

KW - Realizable

KW - Score sequence

KW - Tournament

UR - http://www.scopus.com/inward/record.url?scp=34548822976&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34548822976&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:34548822976

SP - 3403

EP - 3406

BT - Proceedings - IEEE International Symposium on Circuits and Systems

ER -