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SCORE SETS IN k-PARTITE TOURNAMENTS
Pirzada, S.,Naikoo, T.A. 한국전산응용수학회 2006 Journal of applied mathematics & informatics Vol.22 No.1
The set S of distinct scores (outdegrees) of the vertices of a k-partite tournament T($X_l,\;X_2, ..., X_k$) is called its score set. In this paper, we prove that every set of n non-negative integers, except {0} and {0, 1}, is a score set of some 3-partite tournament. We also prove that every set of n non-negative integers is a score set of some k-partite tournament for every $n{\ge}k{\ge}2$.
SCORE SEQUENCES IN ORIENTED GRAPHS
Pirzada, S.,Naikoo, T.A.,Shah, N.A. 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.23 No.1
An oriented graph is a digraph with no symmetric pairs of directed arcs and without loops. The score of a vertex $v_i$ in an oriented graph D is $a_{v_i}\;(or\;simply\;a_i)=n-1+d_{v_i}^+-d_{v_i}^-,\;where\; d_{v_i}^+\;and\;d_{v_i}^-$ are the outdegree and indegree, respectively, of $v_i$ and n is the number of vertices in D. In this paper, we give a new proof of Avery's theorem and obtain some stronger inequalities for scores in oriented graphs. We also characterize strongly transitive oriented graphs.
Score sequences in oriented graphs
S. PIRZADA,T. A. NAIKOO,N. A. SHAH 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.23 No.1
An oriented graph is a digraph with no symmetric pairs of directed arcs and without loops. The score of a vertex vi in an oriented graph D is avi ( or simply ai) = n − 1 + d+vi − d−vi , where d+vi and d−vi are the outdegree and indegree, respectively, of vi and n is the number of vertices in D. In this paper, we give a new proof of Avery’s theorem and obtain some stronger inequalities for scores in oriented graphs. We also characterize strongly transitive oriented graphs.
Score sets in partite tournaments
S. Pirzada,T. A. Naikoo 한국전산응용수학회 2006 Journal of applied mathematics & informatics Vol.22 No.1-2
The set S of distinct scores (outdegrees) of the vertices of a kpartite tournament T(X1,X2, · · · ,Xk) is called its score set. In this paper, we prove that every set of n non-negative integers, except {0} and {0, 1}, is a score set of some 3-partite tournament. We also prove that every set of n non-negative integers is a score set of some k-partite tournament for every n k 2.