On 3-pushdown graphs with large separators


For an integers letl s (n), thes-iterated logarithm function, be defined inductively:l 0 (n)=n,l s+1 (n)=log2 (l 2 (n)) fors≧0. We show that for every fixeds and alln large enough, there is ann-vertex 3-pushdown graph whose smallest separator contains at leastΩ(n/l s (n)) vertices.

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The work of the first author was supported in part by NSF Grants MCS-83-03139, DCR-85-11713 and CCR-86-05353.

The work of the second author was supported in part by NSF Grants MCS-84-16190.

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Galil, Z., Kannan, R. & Szemerédi, E. On 3-pushdown graphs with large separators. Combinatorica 9, 9–19 (1989). https://doi.org/10.1007/BF02122679

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AMS subject classification (1980)

  • 05C35
  • 68C25
  • 68C40