Tomas Feder, Rajeev Motwani

We show how to find in Hamiltonian graphs a cycle of length

$n^{\Omega(1/\log\log n)}$. This is a consequence of a more general

result in which we show that if $G$ has maximum degree $d$ and has a

cycle with $k$ vertices (or a 3-cyclable minor $H$ with $k$ vertices),

then ...
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Kazuo Iwama, Suguru Tamaki

The planar Hajos calculus is the Hajos calculus with the restriction that all the graphs that appear in the construction (including a final graph) must be planar. We prove that the planar Hajos calculus is polynomially bounded iff the HajĀLos calculus is polynomially bounded.

more >>>Ryo Ashida, Tatsuya Imai, Kotaro Nakagawa, A. Pavan, Vinodchandran Variyam, Osamu Watanabe

In [12] (CCC 2013), the authors presented an algorithm for the reachability problem over directed planar graphs that runs in polynomial-time and uses $O(n^{1/2+\epsilon})$ space. A critical ingredient of their algorithm is a polynomial-time, $\tldO(\sqrt{n})$-space algorithm to compute a separator of a planar graph. The conference version provided a sketch ... more >>>