Graph classes characterized both by forbidden subgraphs and degree sequences

  title={Graph classes characterized both by forbidden subgraphs and degree sequences},
  author={Michael D. Barrus and Mohit Kumbhat and Stephen G. Hartke},
  journal={Journal of Graph Theory},
Given a set F of graphs, a graph G is F-free if G does not contain any member of F as an induced subgraph. We say that F is a degree-sequence-forcing set if, for each graph G in the class C of F-free graphs, every realization of the degree sequence of G is also in C. We give a complete characterization of the degree-sequence-forcing sets F when F has cardinality at most two. Mathematics Subject Classification (2000): 05C75, 05C07 

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