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

In this paper, we give a lower bound for the maximum and minimum genus of amultibranched surface by the first Betti number and the minimum and maximumgenus of the boundary of the neighborhood of it, respectively. As itsapplication, we show that the maximum and minimum genus of $G\times S^1$ isequal to twice of the maximum and minimum genus of $G$ for a graph $G$,respectively. This provides an interplay between graph theory and 3-manifoldtheory.

The maximum and minimum genus of a multibranched surface