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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The Weighted Vertex Integrity (wVI) problem takes as input an \(n\)-vertex graph \(G\), a weight function \(w:V(G)\rightarrow \mathbb {N}\), and an integer \(p\). The task is to decide if there exists a set \(X\subseteq V(G)\) such that the weight of \(X\) plus the weight of a heaviest component of \(G-X\) is at most \(p\). Among other results, we prove that:  (1)  wVI is NP-complete on co-comparability graphs, even if each vertex has weight \(1\);     (2)  wVI can be solved in \(O(p^{p+1}n)\) time;     (3)  wVI admits a kernel with at most \(p^3\) vertices.       Result (1) refutes a conjecture by Ray and Deogun (J. Combin. Math. Combin. Comput. 16: 65–73, 1994) and answers an open question by Ray et al. (Ars Comb. 79: 77–95, 2006). It also complements a result by Kratsch et al. (Discr. Appl. Math. 77: 259–270, 1997), stating that the unweighted version of the problem can be solved in polynomial time on co-comparability graphs of bounded dimension, provided that an intersection model of the input graph is given as part of the input.

On the Computational Complexity of Vertex Integrity and Component Order Connectivity