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 an edge-colored graph with $n$ vertices. A subgraph $H$ of $G$ iscalled a rainbow subgraph of $G$ if the colors of each pair of the edges in$E(H)$ are distinct. We define the minimum color degree of $G$ to be thesmallest number of the colors of the edges that are incident to a vertex $v$,for all $v\in V(G)$. Suppose that $G$ contains no rainbow-cycle subgraph oflength four. We show that if the minimum color degree of $G$ is at least$\frac{n+3k-2}{2}$, then $G$ contains a rainbow-cycle subgraph of length atleast $k$, where $k\geq 5$. Moreover, if the condition of $G$ is restricted toa triangle-free graph that contains a rainbow path of length at least$\frac{3k}{2}$, then the lower bound of the minimum color degree of $G$ thatguarantees an existence of a rainbow-cycle subgraph of length to at least $k$can be reduced to $\frac{2n+3k-1}{4}$.

The minimum color degree and a large rainbow cycle in an edge-colored graph