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Score Sequence Pair Problems of (r_{11}, r_{12}, r_{22})TournamentsDetermination of Realizability
Masaya TAKAHASHI Takahiro WATANABE Takeshi YOSHIMURA
Publication
IEICE TRANSACTIONS on Information and Systems
Vol.E90D
No.2
pp.440448 Publication Date: 2007/02/01
Online ISSN: 17451361
DOI: 10.1093/ietisy/e90d.2.440
Print ISSN: 09168532 Type of Manuscript: Special Section PAPER (Special Section on Foundations of Computer Science) Category: Graph Algorithms Keyword: algorithm, graph theory, prescribed degrees, score sequence, tournament,
Full Text: PDF>>
Summary:
Let G be any graph with property P (for example, general graph, directed graph, etc.) and S be nonnegative and nondecreasing 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): (1) G is a directed graph with two disjoint vertex sets A and B. (2) There are r_{11} (r_{22}, respectively) directed edges between every pair of vertices in A(B), and r_{12} directed edges between every pair of vertex in A and vertex in B. Then G is called an (r_{11}, r_{12}, r_{22})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.

