T. A. Naikoo

SCORE SEQUENCES IN ORIENTED GRAPHS

AbstractAn oriented graph is a digraph with no symmetric pairs of directed arcs and without loops. The score of a vertexvi in an oriented graph D is

Score Lists in Tripartite Hypertournaments

a_{v_i }

Imbalances in directed multigraphs

(or simply ai)

SCORE SETS IN k-PARTITE TOURNAMENTS

d_{v_i }^ -

Signed degree sets in signed bipartite graphs

are the outdegree and indegree, respectively, ofvi 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.

Последовательности очков в

The set S of distinct scores (outdegrees) of the vertices of ak-partite tournamentT(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 ofn non-negative integers is a score set of somek-partite tournament for everyn ≥k ≥ 2.