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- W155676707 abstract "Let $D=(V,A)$ be an acyclic digraph. For $xin V$ define $e_{_{D}}(x)$ to be the difference of the indegree and the outdegree of $x$. An acyclic ordering of the vertices of $D$ is a one-to-one map $g: V rightarrow [1,|V|] $ that has the property that for all $x,yin V$ if $(x,y)in A$, then $g(x) < g(y)$. We prove that for every acyclic ordering $g$ of $D$ the following inequality holds: [sum_{xin V} e_{_{D}}(x)cdot g(x) ~geq~ frac{1}{2} sum_{xin V}[e_{_{D}}(x)]^2~.] The class of acyclic digraphs for which equality holds is determined as the class of comparability digraphs of posets of order dimension two." @default.
- W155676707 created "2016-06-24" @default.
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- W155676707 date "2018-01-29" @default.
- W155676707 modified "2023-09-27" @default.
- W155676707 title "Some inequalities for orderings of acyclic digraphs" @default.
- W155676707 doi "https://doi.org/10.11575/cdm.v13i1.62554" @default.
- W155676707 hasPublicationYear "2018" @default.
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