Abstract
AbstractAssume that D is a digraph without cyclic triangles and its vertices are partitioned into classes A1, …, At of independent vertices. A set is called a dominating set of size |S| if for any vertex there is a w∈U such that (w, v)∈E(D). Let β(D) be the cardinality of the largest independent set of D whose vertices are from different partite classes of D. Our main result says that there exists a h = h(β(D)) such that D has a dominating set of size at most h. This result is applied to settle a problem related to generalized Gallai colorings, edge colorings of graphs without 3‐colored triangles. © 2011 Wiley Periodicals, Inc. J Graph Theory
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