Timeline for Infinite graph with no minimal vertex cover
Current License: CC BY-SA 4.0
6 events
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| Mar 4, 2021 at 9:04 | comment | added | bof | A hypergraph with infinite edges need not have a minimal vertex cover or a maximal independent set. Counterexamples abound. If $V$ is an infinite set and the edges are the infinite subsets of $V$, then the independent sets are the finite subsets of $V$. | |
| Mar 4, 2021 at 8:33 | comment | added | Dominic van der Zypen | Can't the argument also been taken to hypergraphs with arbitrary non-empty edges that are not necessarily finite? I mean the argument about a maximal independent set - which, as you write, converts to an argument about a minimal covering set. | |
| Mar 4, 2021 at 7:04 | history | edited | bof | CC BY-SA 4.0 |
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| Mar 4, 2021 at 6:51 | history | edited | bof | CC BY-SA 4.0 |
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| Mar 4, 2021 at 6:44 | history | edited | bof | CC BY-SA 4.0 |
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| Mar 4, 2021 at 4:51 | history | answered | bof | CC BY-SA 4.0 |