Editing Jordan curve theorem (section)

== Computational aspects ==
Adler, Daskalakis and Demaine<ref>{{Cite journal |last1=Adler |first1=Aviv |last2=Daskalakis |first2=Constantinos |last3=Demaine |first3=Erik D. |date=2016 |editor-last=Chatzigiannakis |editor-first=Ioannis |editor2-last=Mitzenmacher |editor2-first=Michael |editor3-last=Rabani |editor3-first=Yuval |editor4-last=Sangiorgi |editor4-first=Davide |title=The Complexity of Hex and the Jordan Curve Theorem |url=http://drops.dagstuhl.de/opus/volltexte/2016/6303 |journal=43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016) |series=Leibniz International Proceedings in Informatics (LIPIcs) |location=Dagstuhl, Germany |publisher=Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik |volume=55 |pages=24:1–24:14 |doi=10.4230/LIPIcs.ICALP.2016.24 |doi-access=free |isbn=978-3-95977-013-2}}</ref> prove that a computational version of Jordan's theorem is [[PPAD complete|PPAD-complete]]. As a corollary, they show that Jordan's theorem implies the [[Brouwer fixed-point theorem]]. This complements the earlier result by Maehara, that Brouwer's fixed point theorem implies Jordan's theorem.{{sfnp|Maehara|1984}}