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

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 |{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.

Original language English IEEE Asia-Pacific Conference on Circuits and Systems, Proceedings, APCCAS 1019-1022 4 https://doi.org/10.1109/APCCAS.2006.342261 Published - 2006 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 06/12/4 → 06/12/6

Directed graphs

### Keywords

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

### ASJC Scopus subject areas

• Engineering(all)

### Cite this

Takahashi, M., Watanabe, T., & Yoshimura, T. (2006). Realizability of Score sequence pair of an (r11, r12, r22)-tournament. In IEEE Asia-Pacific Conference on Circuits and Systems, Proceedings, APCCAS (pp. 1019-1022).  https://doi.org/10.1109/APCCAS.2006.342261

Realizability of Score sequence pair of an (r11, r12, r22)-tournament. / Takahashi, Masaya; Watanabe, Takahiro; Yoshimura, Takeshi.

IEEE Asia-Pacific Conference on Circuits and Systems, Proceedings, APCCAS. 2006. p. 1019-1022 4145569.

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

Takahashi, M, Watanabe, T & Yoshimura, T 2006, Realizability of Score sequence pair of an (r11, r12, r22)-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
Takahashi M, Watanabe T, Yoshimura T. Realizability of Score sequence pair of an (r11, r12, r22)-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
Takahashi, Masaya ; Watanabe, Takahiro ; Yoshimura, Takeshi. / Realizability of Score sequence pair of an (r11, r12, r22)-tournament. IEEE Asia-Pacific Conference on Circuits and Systems, Proceedings, APCCAS. 2006. pp. 1019-1022
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