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 keyring is a graph obtained from a cycle by appending $r\ge0$ leaves to oneof its vertices. Sidorenko proved an Erd\H{o}s-Gallai-type theorem: Every graphof order $n$ and size more than $\frac{(k-1)n}{2}$ contains a keyring of sizeat least $k$ and with $r$ leaves for $r\le\frac{k-1}2$ (Theorem 1.4, AnErd\H{o}s-Gallai-type theorem for keyrings, Graphs Combin., 2018). In thisnote, we show that Sidorenko's theorem holds for larger $r$ and so complete theErd\H{o}s-Gallai-type theorem for keyrings.

An Erd\H{o}s-Gallai-type theorem for keyrings with larger number of leaves