13-homogeneous dendrites

A continuum is a nondegenerate compact connected metric space. A dendrite is a locally connected continuum containing no simple closed curves. A continuum X is said to be 13-homogeneous if there exist three nonempty and mutually disjoint subsets O1,O2 and O3 of X such that X=O1∪O2∪O3 and for each x,y∈X there exists a homeomorphism h:X→X such that h(x)=y if and only if x,y∈Oi for some i∈{1,2,3}. In 2006 V. Neumann-Lara, P. Pellicer-Covarrubias, and I. Puga showed that a dendrite X is 12-homogeneous if and only if X is an arc. The purpose of this paper is to extend this result and classify all 13-homogeneous dendrites.