Let $\mathcal{ F}$ be a family of fixed graphs and let $d$ be large enough. For every $d$-regular graph $G$, we study the existence of a spanning $\mathcal{ F}$-free subgraph of $G$ with large minimum degree. This problem is well-understood if $\mathcal{ F}$ does not contain bipartite graphs. Here we provide asymptotically tight results for many families of bipartite graphs such as cycles or complete bipartite graphs.
Categories: math.CO