Let us say two (simple) graphs G, G' are degree-equivalent if they have the same vertex set, and for every vertex, its degrees in G and in G' are equal. In the early 1980's, S.B. Rao made the conjecture that in any infinite set of graphs, there exist two of them, say G and H, such that H is isomorphic to an induced subgraph of some graph that is degree-equivalent to G. We prove this conjecture.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Graph structure theory
- Induced subgraph