On the acyclic point-connectivity of the n-cube
The acyclic point-connectivity of a graph G, denoted α(G), is the minimum number of points whose removal from G results in an acyclic graph. In a 1975 paper, Harary stated erroneously that α(Qn)=2n−1−1 where Qn denotes the n-cube. We prove that for n>4, 7⋅2n−4≤α(Qn)≤2n−1−2n−y−2, where y=[log2(n−1...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1982-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171282000684 |
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| Summary: | The acyclic point-connectivity of a graph G, denoted α(G), is the minimum number of points whose removal from G results in an acyclic graph. In a 1975 paper, Harary stated erroneously that α(Qn)=2n−1−1 where Qn denotes the n-cube. We prove that for n>4, 7⋅2n−4≤α(Qn)≤2n−1−2n−y−2, where y=[log2(n−1)]. We show that the upper bound is obtained for n≤8 and conjecture that it is obtained for all n. |
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| ISSN: | 0161-1712 1687-0425 |