On 3-pushdown graphs with large separators

For an integers letls(n), thes-iterated logarithm function, be defined inductively:l0(n)=n,ls+1(n)=log2 (l2(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/ls(n)) vertices.

[1]  Maciej M. Syslo,et al.  Characterizations of outerplanar graphs , 1979, Discret. Math..

[2]  Brenda S. Baker,et al.  Approximation algorithms for NP-complete problems on planar graphs , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[3]  Bela Bollobas,et al.  Graph theory , 1979 .

[4]  Mihalis Yannakakis,et al.  Four pages are necessary and sufficient for planar graphs , 1986, Symposium on the Theory of Computing.

[5]  Endre Szemerédi,et al.  On nontrivial separators for k-page graphs and simulations by nondeterministic one-tape Turing machines , 1986, STOC '86.

[6]  Robert E. Tarjan,et al.  Applications of a planar separator theorem , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[7]  Ravi Kannan,et al.  Unraveling k-page graphs , 1985, Inf. Control..

[8]  Leslie G. Valiant,et al.  On Time Versus Space , 1977, JACM.

[9]  Leslie G. Valiant,et al.  Graph-Theoretic Properties in computational Complexity , 1976, J. Comput. Syst. Sci..

[10]  Peter W. Shor,et al.  On the pagenumber of planar graphs , 1984, STOC '84.

[11]  Arnold L. Rosenberg,et al.  The Diogenes Approach to Testable Fault-Tolerant Arrays of Processors , 1983, IEEE Transactions on Computers.

[12]  W. Maass.  Combinatorial lower bound arguments for deterministic and nondeterministic Turing machines , 1985 .

[13]  Arnold L. Rosenberg,et al.  Embedding graphs in books: a layout problem with applications to VLSI design , 1985 .

[14]  Lenwood S. Heath.  Embedding Planar Graphs in Seven Pages , 1984, FOCS.