Abstract
There are 2n-1 ways in which a tree on n vertices can be oriented. Each of these can be regarded as the (Hasse) diagram of a partially ordered set. The maximal and minimal widths of these posets are determined. The maximal width depends on the bipartition of the tree as a bipartite graph and it can be determined in time O(n). The minimal width is one of [λ/2] or [λ/2]+1, where λ is the number of leaves of the tree. An algorithm of execution time O(n + λ2 log λ) to construct the minimal width orientation is given.
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Communicated by I. Rival
This research was partially funded by the National Science and Engineering Research Council of Canada under Grant Number A4219.
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Atkinson, M.D., Ng, D.T.H. On the width of an orientation of a tree. Order 5, 33–43 (1988). https://doi.org/10.1007/BF00143896
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DOI: https://doi.org/10.1007/BF00143896