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

Call a colouring of a graph distinguishing if the only automorphism whichpreserves it is the identity. We investigate the role of the Axiom of Choice inthe existence of certain proper or distinguishing colourings in both vertex andedge variants with special emphasis on locally finite connected graphs. We showthat every locally finite connected graph has a distinguishing colouring withat most countable number of colours or every locally finite connected graph hasa proper colouring with at most countable number of colours if and only ifK\H{o}nig's Lemma holds. This statement holds for both vertex and edgecolourings. Furthermore, we show that it is not provable in ZF that suchcolourings exist even for every connected graph with maximum degree 3. We alsoformulate a few conditions about distinguishing and proper colourings which areequivalent to the Axiom of Choice.

The role of the Axiom of Choice in proper and distinguishing colourings