Forests and score vectors

Combinatorica volume 1, pages49–54(1981)Cite this article

Abstract

Thescore vector of a labeled digraph is the vector of out-degrees of its vertices. LetG be a finite labeled undirected graph without loops, and let σ(G) be the set of distinct score vectors arising from all possible orientations ofG. Let ϕ(G) be the set of subgraphs ofG which are forests of labeled trees. We display a bijection between σ(G) and ϕ(G).

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Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, 02139, Cambridge, Mass., USA

    Daniel J. Kleitman & Kenneth J. Winston

Authors
  1. Daniel J. Kleitman
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  2. Kenneth J. Winston
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Supported in part by ONR Contract N00014-76-C-0366.

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Kleitman, D.J., Winston, K.J. Forests and score vectors. Combinatorica 1, 49–54 (1981). https://doi.org/10.1007/BF02579176

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AMS subject classification (1980)

  • 05 C 20
  • 05 C 05
  • 05 C 30