Is there an English translation of Kuratowski's theorem on forbidden minors of planar graphs? - MathOverflow most recent 30 from http://mathoverflow.net2013-06-19T05:16:55Zhttp://mathoverflow.net/feeds/question/9704http://www.creativecommons.org/licenses/by-nc/2.5/rdfhttp://mathoverflow.net/questions/9704/is-there-an-english-translation-of-kuratowskis-theorem-on-forbidden-minors-of-plIs there an English translation of Kuratowski's theorem on forbidden minors of planar graphs?adamo2009-12-24T21:18:11Z2010-05-04T23:42:44Z
<p>Is there an English translation of Kuratowski's proof about planar graphs?</p>
http://mathoverflow.net/questions/9704/is-there-an-english-translation-of-kuratowskis-theorem-on-forbidden-minors-of-pl/9706#9706Answer by Gjergji Zaimi for Is there an English translation of Kuratowski's theorem on forbidden minors of planar graphs?Gjergji Zaimi2009-12-24T21:57:33Z2009-12-24T21:57:33Z<p>In case you are asking for the original paper "Sur le problème des courbes gauches en Topologie" by Kuratowski where he first proves his characterization of planar graphs, then a translation by J.Jaworowski can be found in "Graph Theory, Łagów", 1981, M. Borowiecki, J. W. Kennedy and M. M. Sysło. It is the proceedings of a conference held in Łagów, dedicated to the memory of K.Kuratowski.</p>
http://mathoverflow.net/questions/9704/is-there-an-english-translation-of-kuratowskis-theorem-on-forbidden-minors-of-pl/9709#9709Answer by Scott Morrison for Is there an English translation of Kuratowski's theorem on forbidden minors of planar graphs?Scott Morrison2009-12-24T22:08:04Z2010-05-04T23:42:44Z<p>You might just want to read Jim Belk's <a href="http://cornellmath.wordpress.com/2007/07/09/graph-minor-theory-part-4/" rel="nofollow">excellent exposition</a> at the Everything Seminar.</p>
http://mathoverflow.net/questions/9704/is-there-an-english-translation-of-kuratowskis-theorem-on-forbidden-minors-of-pl/9714#9714Answer by Harrison Brown for Is there an English translation of Kuratowski's theorem on forbidden minors of planar graphs?Harrison Brown2009-12-24T22:54:24Z2009-12-24T22:54:24Z<p>Kuratowski's theorem is set as an exercise in Ch. 5 of <em>Combinatorial Problems and Exercises</em> by Lovasz. The problem is given as follows:</p>
<p>Let G be a minimal non-planar graph with all vertices of degree at least 3. Then:</p>
<ol>
<li>G is 3-connected. (This is straightforward; supposing otherwise and removing the cutset we can get a planar embedding of G.)</li>
<li>G contains a cycle with a chord. (Provided hint: Consider a maximum path.)</li>
<li>G is isomorphic to one of $K_5$, $K_{3, 3}$.</li>
<li>Conclude Kuratowski's theorem from part 3.</li>
</ol>
<p>The proof is on pp. 299-301, which fortunately are all viewable in the <a href="http://books.google.com/books?id=e99fXXYx9zcC" rel="nofollow">Google Books preview</a>.</p>