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).
AMS subject classification (1980)05 C 20 05 C 05 05 C 30
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- D. J. Kleitman, The Number of Tournament Score Sequences for a Large Number of Players,Combinatorial Structures and Their Applications, University of Calgary, Alberta, (1969), 209–213.Google Scholar
- N. J. A. Sloane,A Handbook of Integer Sequences, Academic Press, 1973.Google Scholar
- R. Stanley, Decompositions of Rational Convex Polytopes,Proceedings of Symposium on Combinatorial Mathematics and Optimal Design, Colorado State University (June, 1978), to appear.Google Scholar