Abstract
To reduce a graph problem to its planar version, a standard technique is to replace crossings in a drawing of the input graph by planarizing gadgets. We show unconditionally that such a reduction is not possible for the perfect matching problem and also extend this to some other problems related to perfect matching. We further show that there is no planarizing gadget for the Hamiltonian cycle problem.
Work supported in part by the Indo-German DST-DFG program, DFG grant TH 472/4-1 and DST grant DST/CS/20100251.
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Gurjar, R., Korwar, A., Messner, J., Straub, S., Thierauf, T. (2012). Planarizing Gadgets for Perfect Matching Do Not Exist. In: Rovan, B., Sassone, V., Widmayer, P. (eds) Mathematical Foundations of Computer Science 2012. MFCS 2012. Lecture Notes in Computer Science, vol 7464. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32589-2_43
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