Forests and score vectors

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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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