TY - JOUR

T1 - Construction of an (r11, r12, r22)- tournament from a score sequence pair

AU - Takahashi, Masaya

AU - Watanabe, Takahiro

AU - Yoshimura, Takeshi

PY - 2007

Y1 - 2007

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 |{uv}| + |{vu}| = [ r11 if u, v ∈ A r 12 if u, v∈ 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." We proposed the characterizations of a "tournament" and an algorithm for determining in linear time whether a pair of two integer sequences is realizable or not [5]. In this paper, we propose an algorithm for constructing a "tournament" from such a score sequence pair.

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 |{uv}| + |{vu}| = [ r11 if u, v ∈ A r 12 if u, v∈ 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." We proposed the characterizations of a "tournament" and an algorithm for determining in linear time whether a pair of two integer sequences is realizable or not [5]. In this paper, we propose an algorithm for constructing a "tournament" from such a score sequence pair.

KW - Algorithm

KW - Construction

KW - Graph theory

KW - Prescribed degrees

KW - Realizable

KW - Score sequence

KW - Tournament

UR - http://www.scopus.com/inward/record.url?scp=34548822976&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34548822976&partnerID=8YFLogxK

U2 - 10.1109/iscas.2007.378298

DO - 10.1109/iscas.2007.378298

M3 - Conference article

AN - SCOPUS:34548822976

SP - 3403

EP - 3406

JO - Proceedings - IEEE International Symposium on Circuits and Systems

JF - Proceedings - IEEE International Symposium on Circuits and Systems

SN - 0271-4310

M1 - 4253410

T2 - 2007 IEEE International Symposium on Circuits and Systems, ISCAS 2007

Y2 - 27 May 2007 through 30 May 2007

ER -