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Antiregular graphs are universal for trees. (English) Zbl 1088.05505
A graph on $$n$$ vertices is antiregular if its vertex degrees take on $$n-1$$ different values. For every $$n\geq2$$ there is an unique connected antiregular graph on $$n$$ vertices denoted by $$A_n$$. It is proved that every tree is isomorphic to a subgraph of $$A_n$$.

##### MSC:
 05C90 Applications of graph theory 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) 05C17 Perfect graphs 05C05 Trees
##### Keywords:
treshold graph; perfect graph
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