Graph classes characterized both by forbidden subgraphs and degree sequences

: 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.

• Type: Journal
• Year: 2008
• Where: JGT
• Authors: Michael D. Barrus, Mohit Kumbhat, Stephen G. Hartke
• Keywords: Complete Characterization, Degree Sequence, F-free Graphs, JGT 2008