A note on the largest induced matching in graphs avoiding a fixed bipartite graph

TL;DR

This paper proves that in certain regular graphs avoiding a specific bipartite subgraph, there exists a large induced matching proportional to the graph's size and degree, highlighting structural properties of such graphs.

Contribution

It provides a simple proof establishing a lower bound on the size of induced matchings in bipartite-subgraph-free regular graphs.

Findings

Induced matching size is at least proportional to (n/d) log d.

The proof is simpler than previous approaches.

Results apply to graphs avoiding a fixed bipartite subgraph.

Abstract

We give a simple proof that every $n$-vertex graph $d$-regular graph that does not contain a fixed bipartite graph as a subgraph has an induced matching of size $\Omega((n/d)(\log d))$.