Locally-finite connected-homogeneous digraphs

Locally-finite connected-homogeneous digraphs

The classification of finite and locally finite connected-homogeneous digraphs

We classify the finite connected-homogeneous digraphs, as well as the infinite locally finite such digraphs with precisely one end. This completes the classification of all the locally finite connected-homogeneous digraphs.

On locally finite transitive two - ended digraphs *

Since decades transitive graphs are a topic of great interest. The study of s-edge transitive (undirected) graphs goes back to Tutte [13], who showed that finite cubic graphs cannot be s-edge transitive for s> 5. Weiss [14] proved several years later that the only finite connected s-edge transitive graphs with s = 8 are the cycles. Considering directed graphs the situation is much more involved...

More Monotone Open Homogeneous Locally Connected Plane Continua

This paper constructs a continuous decomposition of the Sierpiński curve into acyclic continua one of which is an arc. This decomposition is then used to construct another continuous decomposition of the Sierpiński curve. The resulting decomposition space is homeomorphic to the continuum obtained from taking the Sierpiński curve and identifying two points on the boundary of one of its complemen...

Every Monotone Open 2-homogeneous Metric Continuum Is Locally Connected

In [16, Theorem 3.12, p. 397], Ungar answered a question of Burgess [2] by showing that every 2-homogeneous metric continuum is locally connected. A short, elementary and elegant proof of this result has been given by Whittington [17] who has omitted a powerful result of Effros (viz. Theorem 2.1 of [4, p. 39]) used by Ungar. It is observed in this note that Whittington's proof can be applied to...