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 [5]. In this paper, we propose an algorithm for constructing a "tournament" from such a score sequence pair.

Original languageEnglish
Article number4253410
Pages (from-to)3403-3406
Number of pages4
JournalProceedings - IEEE International Symposium on Circuits and Systems
Publication statusPublished - 2007 Sep 27
Event2007 IEEE International Symposium on Circuits and Systems, ISCAS 2007 - New Orleans, LA, United States
Duration: 2007 May 272007 May 30

Keywords

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

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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