Monotone maps of 𝐺-like continua with positive topological entropy yield indecomposability

In the previous paper [5], we proved that if for any graph G, a homeomorphism on a G-like continuum X has positive topological entropy, then the continuum X contains an indecomposable subcontinuum. Also, if for a tree G, a monotone map on a G-like continuum X has positive topological entropy, then the continuum X contains an indecomposable subcontinuum. In this note, we extend these results. In fact, we prove that if for any graph G, a monotone map on a G-like continuum X has positive topological entropy, then the continuum X contains an indecomposable subcontinuum. Also we study topological entropy of monotone maps on Suslinean continua.