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 $G$ is said to be a $k$-degenerate graph if any subgraph of $G$contains a vertex of degree at most $k$. Let $\kappa$ be any non-negativefunction on the vertex set of $G$. We first define a $\kappa$-degenerate graph.Next we give an efficient algorithm to determine whether a graph is$\kappa$-degenerate. We revisit the concept of dynamic monopolies in graphs.The latter notion is used in formulation and analysis of spread of influencesuch as disease or opinion in social networks. We consider dynamic monopolieswith (not necessarily positive) but integral threshold assignments. We obtain asufficient and necessary relationship between dynamic monopolies andgeneralized degeneracy. As applications of the previous results we consider theproblem of determining the maximum size of $\kappa$-degenerate (or$k$-degenerate) induced subgraphs in any graph. We obtain some upper and lowerbounds for the maximum size of any $\kappa$-degenerate induced subgraph ingeneral and regular graphs. All of our bounds are constructive.

Generalized degeneracy, dynamic monopolies and maximum degenerate subgraphs