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

The monochromatic tree partition number of an $r$-edge-colored graph $G$,denoted by $t_r(G)$, is the minimum integer $k$ such that whenever the edges of$G$ are colored with $r$ colors, the vertices of $G$ can be covered by at most$k$ vertex-disjoint monochromatic trees. In general, to determine this numberis very difficult. For 2-edge-colored complete multipartite graph, Kaneko,Kano, and Suzuki gave the exact value of $t_2(K(n_1,n_2,...,n_k))$. In thispaper, we prove that if $n\geq 3$, and K(n,n) is 3-edge-colored such that everyvertex has color degree 3, then $t_3(K(n,n))=3.$

Partitioning 3-edge-colored complete equi-bipartite graphs by monochromatic trees under a color degree condition