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Paper Abstract and Keywords
Presentation 2006-01-11 14:00
Score Sequence Pair Problems of (r11,r12,r22)-Tournaments -- Construction --
Masaya Takahashi (Fukuoka Inst. of Tech./Waseda Univ), Takahiro Watanabe, Takeshi Yoshimura (Waseda Univ)
Abstract (in Japanese) (See Japanese page) 
(in English) Let G be any graph with the 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 by many researchers, such as Erdös, Harary. 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 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, r12, 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 problem is “yes.” This problem has important applications such as the communication network control problems. Recently, we proposed the algorithm for determining in linear time whether a pair of two integer sequences is realizable or not. However the following problem remains: Construct such the tournament efficiency from a score sequence pair. Solving this problem is very important for the application described above.
In this paper, we propose an optimal time algorithm for constructing such a tournament.
Keyword (in Japanese) (See Japanese page) 
(in English) algorithm / graph theory / prescribed degrees / score sequence / realizable / tournament / /  
Reference Info. IEICE Tech. Rep., vol. 105, no. 502, CAS2005-70, pp. 1-6, Jan. 2006.
Paper # CAS2005-70 
Date of Issue 2006-01-04 (CAS) 
ISSN Print edition: ISSN 0913-5685
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Conference Information
Committee CAS  
Conference Date 2006-01-11 - 2006-01-13 
Place (in Japanese) (See Japanese page) 
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Paper Information
Registration To CAS 
Conference Code 2006-01-CAS 
Language English 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Score Sequence Pair Problems of (r11,r12,r22)-Tournaments 
Sub Title (in English) Construction 
Keyword(1) algorithm  
Keyword(2) graph theory  
Keyword(3) prescribed degrees  
Keyword(4) score sequence  
Keyword(5) realizable  
Keyword(6) tournament  
1st Author's Name Masaya Takahashi  
1st Author's Affiliation Fukuoka Institute of Technology (Fukuoka Inst. of Tech./Waseda Univ)
2nd Author's Name Takahiro Watanabe  
2nd Author's Affiliation Waseda University (Waseda Univ)
3rd Author's Name Takeshi Yoshimura  
3rd Author's Affiliation Waseda University (Waseda Univ)
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Date Time 2006-01-11 14:00:00 
Presentation Time 25 minutes 
Registration for CAS 
Paper # CAS2005-70 
Volume (vol) vol.105 
Number (no) no.502 
Page pp.1-6 
Date of Issue 2006-01-04 (CAS) 

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