We prove that for every graph H, there exists ε>0 such that every n-vertex graph with no vertex-minors isomorphic to H has a pair of disjoint sets A, B of vertices such that |A|,|B|≥εn and A is complete or anticomplete to B. We deduce this from recent work of Chudnovsky, Scott, Seymour, and Spirkl (2018). This proves the analog of the Erdős–Hajnal conjecture for vertex-minors.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Erdős–Hajnal conjecture