Computing Maximum Unavoidable Subgraphs Using SAT Solvers

Unavoidable subgraphs have been widely studied in the context of Ramsey Theory. The research in this area focuses on highly structured graphs such as cliques, cycles, paths, stars, trees, and wheels. We propose to study maximum unavoidable subgraphs measuring the size in the number of edges. We computed maximum unavoidable subgraphs for graphs up to order nine via SAT solving and observed that these subgraphs are less structured, although all are bipartite. Additionally, we found large unavoidable bipartite subgraphs up to order twelve. We also present the concept of multi-component unavoidable subgraphs and show that large multi-component subgraphs are unavoidable in small graphs. We envision that maximum unavoidable subgraphs can be exploited using an alternative approach to breaking graph symmetries.