Revisiting Extremal Graphs Having No Stable Cutsets
| Autor: | Rauch, Johannes, Rautenbach, Dieter |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Confirming a conjecture posed by Caro, it was shown by Chen and Yu that every graph $G$ with $n$ vertices and at most $2n-4$ edges has a stable cutset, which is a stable set of vertices whose removal disconnects the graph. Le and Pfender showed that all graphs with $n$ vertices and $2n-3$ edges without stable cutset arise recursively glueing together triangles and triangular prisms along an edge or triangle. Le and Pfender's proof contains a gap, which we fill in the present article. |
| Databáze: | arXiv |
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