We consider a two player game on a progressively and locally finite directed graph and we prove that the first player wins if and only if the graph has a local kernel. The result is sharp. From it, we derive a short proof of a general version of the Galeana-Sanchez & Neuman-Lara Theorem that give a
On the existence of kernels and h-kernels in directed graphs
✍ Scribed by H. Galeana-Sánchez
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 272 KB
- Volume
- 110
- Category
- Article
- ISSN
- 0012-365X
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In Section 1, we survey the existence theorems for a kernel; in Section 2, we discuss a new conjecture which could constitute a bridge between the kernel problems and the perfect graph conjecture. In fact, we believe that a graph is 'quasi-perfect' if and only if it is perfect. ## Proposition 1.1.
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