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

Let $G$ be a graph with $X\subseteq V(G)$ and let $l$ be an intersectingsupermodular subadditive integer-valued function on subsets of $V(G)$. Thegraph $G$ is said to be $l$-partition-connected, if for every partition $P$ of$V(G)$, $e_G(P)\ge \sum_{A\in P} l(A)-l(V(G))$, where $e_G(P)$ denotes thenumber of edges of $G$ joining different parts of $P$. Let $\lambda \in [0,1]$be a real number and let $\eta $ be a real function on $X$. In this paper, weshow that if $G$ is $l$-partition-connected and for all $S\subseteq X$,$$\Theta_l(G \setminus S) \le \sum_{v\in S} (\eta(v)-2l(v))+l(V(G))+l(S)-\lambda (e_G(S))+l(S)),$$ then $G$ has an$l$-partition-connected spanning subgraph $H$ such that for each vertex $v\inX$, $d_H(v)\le \lceil \eta(v) -\lambda l(v) \rceil $, where $e_G(S)$ denotesthe number of edges of $G$ with both ends in $S$ and $\Theta_l(G \setminus S)$denotes the maximum number of all $\sum_{A\in P} l(A)-e_{G\setminus S}(P)$taken over all partitions $P$ of $V(G)\setminus S$. Finally, we show that if$H$ is an $(l_1+\cdots +l_m)$-partition-connected graph, then it can bedecomposed into $m$ edge-disjoint spanning subgraphs $H_1,\ldots, H_m$ suchthat every graph $H_i$ is $l_i$-partition-connected, where $l_1, l_2,\ldots,l_m$ are $m$ intersecting supermodular subadditive integer-valued functions onsubsets of $V(H)$. These results generalize several known results.

Packing spanning partition-connected subgraphs with small degrees