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Tripartite graphs with given degree set. (English) Zbl 1317.05032
Summary: If $$k\geq 1$$, then the global degree set of a k-partite graph $$G=(V_1,V_2,\dots, V_k,E)$$ is the set of the distinct degrees of the vertices of $$G$$, while if $$k\geq 2$$, then the distributed degree set of $$G$$ is the family of the $$k$$ degree sets of the vertices of the parts of $$G$$. We propose algorithms to construct bipartite and tripartite graphs with prescribed global and distributed degree sets consisting from arbitrary nonnegative integers. We also present a review of the similar known results on digraphs.
##### MSC:
 05C07 Vertex degrees
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