All reports by Author Jakub Opršal:

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TR19-092
| 9th July 2019
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Venkatesan Guruswami, Jakub Opršal, Sai Sandeep#### Revisiting Alphabet Reduction in Dinur's PCP

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TR19-053
| 5th April 2019
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Andrei Krokhin, Jakub Opršal#### The complexity of 3-colouring $H$-colourable graphs

Venkatesan Guruswami, Jakub Opršal, Sai Sandeep

Dinur's celebrated proof of the PCP theorem alternates two main steps in several iterations: gap amplification to increase the soundness gap by a large constant factor (at the expense of much larger alphabet size), and a composition step that brings back the alphabet size to an absolute constant (at the ... more >>>

Andrei Krokhin, Jakub Opršal

We study the complexity of approximation on satisfiable instances for graph homomorphism problems. For a fixed graph $H$, the $H$-colouring problem is to decide whether a given graph has a homomorphism to $H$. By a result of Hell and Nešet?il, this problem is NP-hard for any non-bipartite graph $H$. In ... more >>>