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

Masaya Takahashi, Takahiro Watanabe, Takeshi Yoshimura

Research output: Chapter in Book/Report/Conference proceedingConference contribution

### 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 Proceedings - IEEE International Symposium on Circuits and Systems 3403-3406 4 Published - 2007 2007 IEEE International Symposium on Circuits and Systems, ISCAS 2007 - New Orleans, LA, United StatesDuration: 2007 May 27 → 2007 May 30

### Other

Other 2007 IEEE International Symposium on Circuits and Systems, ISCAS 2007 United States New Orleans, LA 07/5/27 → 07/5/30

Directed graphs

### 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

Takahashi, M., Watanabe, T., & Yoshimura, T. (2007). Construction of an (r 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.

Proceedings - IEEE International Symposium on Circuits and Systems. 2007. p. 3403-3406 4253410.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Takahashi, M, Watanabe, T & Yoshimura, T 2007, Construction of an (r 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.
Takahashi M, Watanabe T, Yoshimura T. Construction of an (r 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
Takahashi, Masaya ; Watanabe, Takahiro ; Yoshimura, Takeshi. / Construction of an (r 11, r 12, r 22)- tournament from a score sequence pair Proceedings - IEEE International Symposium on Circuits and Systems. 2007. pp. 3403-3406
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