| Autor: |
Acharya, B. D., Germina, K. A., Abhishek, Kumar, Rao, S. B., Zaslavsky, T. |
| Rok vydání: |
2010 |
| Předmět: |
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| Zdroj: |
Indian Journal of Mathematics, 51 (2009), no. 3, 597-609. MR 2573808 (2011b:05082). Zbl 1194.05053 |
| Druh dokumentu: |
Working Paper |
| Popis: |
In a digraph $D = (X, \mathcal{U})$, not necessarily finite, an arc $(x, y) \in \mathcal{U}$ is reachable from a vertex $u$ if there exists a directed walk $W$ that originates from $u$ and contains $(x, y)$. A subset $S \subseteq X$ is an arc-reaching set of $D$ if for every arc $(x, y)$ there exists a diwalk $W$ originating at a vertex $u \in S$ and containing $(x, y)$. A minimal arc-reaching set is an arc-basis. $S$ is a point-reaching set if for every vertex $v$ there exists a diwalk $W$ to $v$ originating at a vertex $u \in S$. A minimal point-reaching set is a point-basis. We extend the results of Harary, Norman, and Cartwright on point-bases in finite digraphs to point- and arc-bases in infinite digraphs. |
| Databáze: |
arXiv |
| Externí odkaz: |
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