TY - GEN

T1 - Realizability of Score sequence pair of an (r11, r12, r22)-tournament

AU - Takahashi, Masaya

AU - Watanabe, Takahiro

AU - Yoshimura, Takeshi

PY - 2006/12/1

Y1 - 2006/12/1

N2 - 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.

AB - 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.

KW - Algorithm

KW - Graph theory

KW - Prescribed degrees

KW - Realizable

KW - Score sequence

KW - Tournament

UR - http://www.scopus.com/inward/record.url?scp=50249089565&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=50249089565&partnerID=8YFLogxK

U2 - 10.1109/APCCAS.2006.342261

DO - 10.1109/APCCAS.2006.342261

M3 - Conference contribution

AN - SCOPUS:50249089565

SN - 1424403871

SN - 9781424403875

T3 - IEEE Asia-Pacific Conference on Circuits and Systems, Proceedings, APCCAS

SP - 1019

EP - 1022

BT - APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems

T2 - APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems

Y2 - 4 December 2006 through 6 December 2006

ER -