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Directed star decompositions of the complete directed graph
Author(s) -
Colbourn Charles J.,
Hoffman D. G.,
Rodger C. A.
Publication year - 1992
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190160511
Subject(s) - combinatorics , mathematics , directed graph , graph , partition (number theory) , star (game theory) , strongly connected component , discrete mathematics , mathematical analysis
An ( s, t )‐directed star is a directed graph with s + t + 1 vertices and s + t arcs; s vertices have indegree zero and outdegree one, t have indegree one and outdegree zero, and one has indegree s and outdegree t . An ( s, t )‐directed star decomposition is a partition of the arcs of a complete directed graph of order n into ( s, t )‐directed starsx. We establish necessary and sufficient conditions on s, t , and n for an ( s, t )‐directed star decomposition of order n to exist.