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

Let $G$ be a graph and let $f$ be a positive integer-valued function on$V(G)$. Assume that for all $S\subseteq V(G)$, $$\sum_{v\in I(G\setminusS)}f(v)(f(v)+1)\le |S|,$$ where $I(G\setminus S)$ denotes the set of isolatedvertices of $G\setminus S$. In this paper, we show that if for all $S\subseteqV(G)$, $$\omega(G\setminus S)\le \sum_{v\in S}(f(v)-1)+1,$$ and $\sum_{v\inV(G)}f(v)$ is even, then $G$ has a factor $F$ such that for each vertex $v$,$d_F(v)=f(v)$, where $\omega(G\setminus S)$ denotes the number of components of$G\setminus S$. Moreover, we show that if for all $S\subseteq V(G)$,$$\omega(G\setminus S)\le \frac{1}{4}|S|+1,$$ and $f\ge 2$, then $G$ has aconnected factor $H$ such that for each vertex $v$, $d_H(v)\in\{f(v),f(v)+1\}$.

Factors and connected factors in tough graphs with high isolated toughness