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On the bar visibility number of complete bipartite graphs

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 Added by Yan Yang
 Publication date 2019
  fields
and research's language is English




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A $t$-bar visibility representation of a graph assigns each vertex up to $t$ horizontal bars in the plane so that two vertices are adjacent if and only if some bar for one vertex can see some bar for the other via an unobstructed vertical channel of positive width. The least $t$ such that $G$ has a $t$-bar visibility representation is the bar visibility number of $G$, denoted by $b(G)$. For the complete bipartite graph $K_{m,n}$, the lower bound $b(K_{m,n})gelceil{frac{mn+4}{2m+2n}}rceil$ from Eulers Formula is well known. We prove that equality holds.



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