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

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Information Systems
- Computer Graphics and Computer-Aided Design
- Software

### 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

**Score sequence pair problems of (r _{11}, r_{12}, r _{22})-tournaments - Determination of realizability.** / Takahashi, Masaya; Watanabe, Takahiro; Yoshimura, Takeshi.

Research output: Contribution to journal › Article

_{11}, r

_{12}, r

_{22})-tournaments - Determination of realizability',

*IEICE Transactions on Information and Systems*, vol. E90-D, no. 2, pp. 440-447. https://doi.org/10.1093/ietisy/e90-d.2.440

_{11}, r

_{12}, r

_{22})-tournaments - Determination of realizability. IEICE Transactions on Information and Systems. 2007 Feb;E90-D(2):440-447. https://doi.org/10.1093/ietisy/e90-d.2.440

}

TY - JOUR

T1 - Score sequence pair problems of (r11, r12, r 22)-tournaments - Determination of realizability

AU - Takahashi, Masaya

AU - Watanabe, Takahiro

AU - Yoshimura, Takeshi

PY - 2007/2

Y1 - 2007/2

N2 - 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 r11 (r22, respectively) directed edges between every pair of vertices in A(B), and r12 directed edges between every pair of vertex in A and vertex in B. Then G is called an (r11, r 12, r22) -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.

AB - 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 r11 (r22, respectively) directed edges between every pair of vertices in A(B), and r12 directed edges between every pair of vertex in A and vertex in B. Then G is called an (r11, r 12, r22) -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.

KW - Algorithm

KW - Graph theory

KW - Prescribed degrees

KW - Score sequence

KW - Tournament

UR - http://www.scopus.com/inward/record.url?scp=33847163956&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33847163956&partnerID=8YFLogxK

U2 - 10.1093/ietisy/e90-d.2.440

DO - 10.1093/ietisy/e90-d.2.440

M3 - Article

AN - SCOPUS:33847163956

VL - E90-D

SP - 440

EP - 447

JO - IEICE Transactions on Information and Systems

JF - IEICE Transactions on Information and Systems

SN - 0916-8532

IS - 2

ER -