English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

A graph is one-ended if it contains a ray (a one way infinite path) andwhenever we remove a finite number of vertices from the graph then what remainshas only one component which contains rays. A vertex $v$ {\em dominates} a rayin the end if there are infinitely many paths connecting $v$ to the ray suchthat any two of these paths have only the vertex $v$ in common. We prove thatif a one-ended graph contains no ray which is dominated by a vertex and noinfinite family of pairwise disjoint rays, then it has a tree-decompositionsuch that the decomposition tree is one-ended and the tree-decomposition isinvariant under the group of automorphisms.  This can be applied to prove a conjecture of Halin from 2000 that theautomorphism group of such a graph cannot be countably infinite and solves arecent problem of Boutin and Imrich. Furthermore, it implies that everytransitive one-ended graph contains an infinite family of pairwise disjointrays.

On tree-decompositions of one-ended graphs