Graphs with given valences (Q1969656)
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scientific article; zbMATH DE number 1416690
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Graphs with given valences |
scientific article; zbMATH DE number 1416690 |
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Graphs with given valences (English)
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19 March 2000
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The paper contains a short proof of the Gale-Ryser theorem (which states a necessary and sufficient condition for the existence of a \((0,1)\)-matrix with prescribed vectors of row sums and column sums). Furthermore, it is shown that the Gale-Ryser theorem is logically equivalent to the Erdős-Gallai theorem (which states a necessary and sufficient condition for the existence of a graph with prescribed vector of vertex-degrees).
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graph theory
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Gale-Ryser theorem
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Erdős-Gallai theorem
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0.9054074
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0.90327215
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0.8802267
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0.8656249
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