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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This article is built upon three main ideas. First, for a class of monomialideals, it is proven that the multiplicity of an ideal equals the number ofrealizations of its codimension (an intuitive concept that we define later).Next, for an arbitrary graph G, we construct a monomial ideal M_G, and showthat the chromatic number of G is equal to the codimension of M_G. Finally, fora class of graphs, we give a formula that computes the chromatic polynomial ofG, evaluated at the chromatic number of G, in terms of the codimension andmultiplicity of M_G. In particular, the formula applies to all graphssatisfying the Erdos-Faber-Lov\'asz conjecture.

Monomial invariants applied to graph coloring