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

In this note we define and study graph invariants generalizing to higherdimension the maximum degree of a vertex and the vertex-connectivity (our$0$-dimensional cases). These are known to coincide almost surely in any regimefor Erdoes-Renyi random graphs. We show the same in the one dimensional casefor a middle density regime and show the easier inequality for all dimensionsin the same regime. Our original motivation comes from the study of minimalfree resolutions of Stanley-Reisner rings of clique complexes of graphs incommutative algebra, In that setting the higher dimensional vertexconnectivities determine the lengths of the strands. Through our results we aimto replace (asymptotically) vertex connectivity by a simpler invariant.

Higher dimensional connectivity and minimal degree of random graphs with an eye towards minimal free resolutions