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/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

A homogeneous set of an $n$-vertex graph is a set $X$ of vertices ($2\le|X|\le n-1$) such that every vertex not in $X$ is either complete oranticomplete to $X$. A graph is called prime if it has no homogeneous set. Achain of length $t$ is a sequence of $t+1$ vertices such that for every vertexin the sequence except the first one, its immediate predecessor is its uniqueneighbor or its unique non-neighbor among all of its predecessors. We provethat for all $n$, there exists $N$ such that every prime graph with at least$N$ vertices contains one of the following graphs or their complements as aninduced subgraph: (1) the graph obtained from $K_{1,n}$ by subdividing everyedge once, (2) the line graph of $K_{2,n}$, (3) the line graph of the graph in(1), (4) the half-graph of height $n$, (5) a prime graph induced by a chain oflength $n$, (6) two particular graphs obtained from the half-graph of height$n$ by making one side a clique and adding one vertex.

Unavoidable induced subgraphs in large graphs with no homogeneous sets