Date of Original Version
Given a set F of graphs, a graph G is F-free if G does not contain any member of as an induced subgraph. A set F is degree-sequence-forcing (DSF) if, for each graph G in the class C of -free graphs, every realization of the degree sequence of G is also in C. A DSF set is minimal if no proper subset is also DSF. In this paper, we present new properties of minimal DSF sets, including that every graph is in a minimal DSF set and that there are only finitely many DSF sets of cardinality k. Using these properties and a computer search, we characterize the minimal DSF triples.
Barrus, M. D., & Hartke, S. G. (2015). Minimal forbidden sets for degree seuqnce characterizations. Discrete Mathematics. 338(9), 1543-1554.
Available at: http://dx.doi.org/10.1016/j.disc.2015.02.018