Sarah K. Merz

Vertices x and y dominate a tournament T if for all vertices z ≠ x, y, either x beats z or y beats z. Let dom(T) be the graph on the vertices of T with edges between pairs of vertices that dominate T. We show that dom(T) is either an odd cycle with possible pendant vertices or a forest of caterpillars. While this is not a characterization, it does lead to considerable information about dom(T). Since dom(T) is the complement of the competition graph of the tournament formed by reversing the arcs of T, complementary results are obtained for the competition graph of a tournament. © 1998 John Wiley & Sons, Inc. J. Graph Theory 29: 103–110, 1998

In this study, we guide human pluripotent stem cells into multipotent pancreatic progenitors. This common precursor population, which has the ability to mature into acinar, ductal and functional β-cells, serves as a basis for studying developmental processes and deciphering early cancer formation in a cell type-specific context. Using single-cell RNA sequencing and subsequent validation studies, we were able to dissect PP heterogeneity and specific cell-cell communication signals.

The domination graph of a digraph has the same vertices as the digraph with an edge between two vertices if every other vertex loses to at least one of the two. Previously, the authors showed that the domination graph of a tournament is either an odd cycle with or without isolated and/or pendant vertices, or a forest of caterpillars. They also showed that any graph consisting of an odd cycle with or without isolated and/or pendant vertices is the domination graph of some tournament. This paper extends these results to oriented graphs. We also show that any caterpillar is the domination graph of some digraph, but a path on four or more vertices is not the domination graph of any tournament. Other results relate the domination graph of a tournament to its positive subtournament defined by Fisher and Ryan, and the possible and average number of edges in the domination graph of a tournament.