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Seven criteria for integer sequences being graphic. (English) Zbl 0752.05052
A nonincreasing sequence of positive integers with even sum is called graphic when they represent the vertex-degrees of some simple graph. This paper lists seven criteria for such sequences to be graphic, and gives a relatively short proof of their equivalence. The criteria are those due to Ryser, Berge, Erdős-Gallai, Fulkerson-Hoffman-McAndrew, Bollobás, Grünbaum and a simple reformulation of the recent Hässelbarth criterion.

05C99 Graph theory
11B83 Special sequences and polynomials
Full Text: DOI
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