# Construction of an (r11, r12, r22)- tournament from a score sequence pair

Masaya Takahashi, Takahiro Watanabe, Takeshi Yoshimura

Research output: Contribution to journalConference article

### 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}| = [ r11 if u, v ∈ A r 12 if u, v∈ 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." 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 . In this paper, we propose an algorithm for constructing a "tournament" from such a score sequence pair.

Original language English 4253410 3403-3406 4 Proceedings - IEEE International Symposium on Circuits and Systems Published - 2007 Sep 27 2007 IEEE International Symposium on Circuits and Systems, ISCAS 2007 - New Orleans, LA, United StatesDuration: 2007 May 27 → 2007 May 30

### Keywords

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

### ASJC Scopus subject areas

• Electrical and Electronic Engineering