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 languageEnglish
Title of host publicationAPCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems
Pages1019-1022
Number of pages4
DOIs
Publication statusPublished - 2006 Dec 1
EventAPCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems - , Singapore
Duration: 2006 Dec 42006 Dec 6

Publication series

NameIEEE Asia-Pacific Conference on Circuits and Systems, Proceedings, APCCAS

Conference

ConferenceAPCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems
CountrySingapore
Period06/12/406/12/6

Keywords

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

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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    Takahashi, M., Watanabe, T., & Yoshimura, T. (2006). Realizability of Score sequence pair of an (r11, r12, r22)-tournament. In APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems (pp. 1019-1022). [4145569] (IEEE Asia-Pacific Conference on Circuits and Systems, Proceedings, APCCAS). https://doi.org/10.1109/APCCAS.2006.342261