Raghav Kulkarni

The purpose of this paper is to study the deterministic

{\em isolation} for certain structures in directed and undirected

planar graphs.

The motivation behind this work is a recent development on this topic. For example, \cite{btv07} isolate a directed path in planar graphs and

\cite{dkr08} isolate a perfect matching in ...
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Samir Datta, Raghav Kulkarni, Raghunath Tewari

We prove that Perfect Matching in bipartite planar graphs is in UL, improving upon

the previous bound of SPL (see [DKR10]) on its space complexity. We also exhibit space

complexity bounds for some related problems. Summarizing, we show that, constructing:

1. a Perfect Matching in bipartite planar graphs is in ...
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Rohit Gurjar, Arpita Korwar, Jochen Messner, Simon Straub, Thomas Thierauf

To compare the complexity of the perfect matching problem for general graphs with that for planar graphs, one might try to come up with a reduction from the perfect matching problem to the planar perfect matching problem.

The obvious way to construct such a reduction is via a {\em planarizing ...
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Simon Straub, Thomas Thierauf, Fabian Wagner

Counting the number of perfect matchings in arbitrary graphs is a $\#$P-complete problem. However, for some restricted classes of graphs the problem can be solved efficiently. In the case of planar graphs, and even for $K_{3,3}$-free graphs, Vazirani showed that it is in NC$^2$. The technique there is to compute ... more >>>

Dmitry Itsykson, Artur Riazanov

A canonical communication problem ${\rm Search}(\phi)$ is defined for every unsatisfiable CNF $\phi$: an assignment to the variables of $\phi$ is distributed among the communicating parties, they are to find a clause of $\phi$ falsified by this assignment. Lower bounds on the randomized $k$-party communication complexity of ${\rm Search}(\phi)$ in ... more >>>

Per Austrin, Kilian Risse

We study the complexity of proving that a sparse random regular graph on an odd number of vertices does not have a perfect matching, and related problems involving each vertex being matched some pre-specified number of times. We show that this requires proofs of degree $\Omega(n/\log n)$ in the Polynomial ... more >>>