Note on the bisection width of cubic graphs.
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| Title: | Note on the bisection width of cubic graphs. |
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| Authors: | Jobson, Adam S.1 (AUTHOR) adam.jobson@louisville.edu, Kézdy, André E.1 (AUTHOR) andre.kezdy@louisville.edu, Lehel, Jenő1,2 (AUTHOR) lehelj@renyi.hu |
| Source: | Discrete Applied Mathematics. Oct2020, Vol. 285, p434-442. 9p. |
| Subjects: | Parallel processing |
| Abstract: | The bisection width is the minimum number of edges required to split the vertex set of a graph into two (nearly) equal parts. Monien and Preis proved that the bisection width of a cubic graph with n nodes is bounded above by n ∕ 6 + o (n). Here we show that every cubic graph of even order n ≥ 16 has bisection width less than n ∕ 2 , thus these graphs violate the even cut condition (ECC). All edge-minimal subcubic graphs satisfying ECC are also described. The bisection width is a reference parameter to compare networks for parallel architectures; ECC is a property necessary for bottleneck free all-to-all communications. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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