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

Masaya Takahashi, Takahiro Watanabe, Takeshi Yoshimura

Research output: Contribution to journalArticlepeer-review

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 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.

Original languageEnglish
Pages (from-to)440-447
Number of pages8
JournalIEICE Transactions on Information and Systems
VolumeE90-D
Issue number2
DOIs
Publication statusPublished - 2007 Feb

Keywords

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

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering
  • Artificial Intelligence

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