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• W2166201119 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 isin G (u ne v), (G satisfies |{uv}| + |{vu}|) = {( (r <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>11</sub> if u, v isin A) (r <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>12</sub> if u isin A, v isin B) (r <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>22</sub> if u, v isin B)), where uv (vu, respectively) means a directed edges from u to v (from v to u). Then G is called an (r <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>11</sub> , r <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>12</sub> , r <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>22</sub> )-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 (Takahashi et al., 2006). In this paper, we propose an algorithm for constructing a tournament from such a score sequence pair." @default.
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• W2166201119 date "2007-05-01" @default.
• W2166201119 modified "2023-09-26" @default.
• W2166201119 title "Construction of an (r11, r12, r22)-Tournament from a Score Sequence Pair" @default.
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• W2166201119 doi "https://doi.org/10.1109/iscas.2007.378298" @default.
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