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Goal. I would like to tell you a bit about my favorite theorems, ideas or concepts in mathematics and why I like them so much. This time. What is...Hadwiger’s conjecture? Or: Coloring is difficult... Disclaimer. Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references. Slides. http://www.dtubbenhauer.com/youtube.html Thumbnail. https://wallpaperaccess.com/full/2330... Pictures from • What is...the Kuratowski-Wagner theorem? Hadwiger’s Conjecture. Article of Paul Seymour in https://en.wikipedia.org/wiki/Open_Pr... See also https://web.math.princeton.edu/~pds/p... https://en.wikipedia.org/wiki/Hadwige...) https://link.springer.com/article/10.... https://link.springer.com/article/10.... https://www.cambridge.org/core/journa... https://linkinghub.elsevier.com/retri... Background on graphs. https://en.wikipedia.org/wiki/Four_co... https://mathworld.wolfram.com/Four-Co... https://en.wikipedia.org/wiki/Categor... https://en.wikipedia.org/wiki/Graph_m... https://en.wikipedia.org/wiki/Graph_c... Mathematica. https://demonstrations.wolfram.com/Fo... https://demonstrations.wolfram.com/Fo... Pictures used. https://en.wikipedia.org/wiki/Four_co... https://en.wikipedia.org/wiki/Four_co... Pictures from • What is...the Kuratowski-Wagner theorem? https://upload.wikimedia.org/wikipedi... Picture from https://linkinghub.elsevier.com/retri... https://en.wikipedia.org/wiki/Peterse... YouTube and co. • Luke Postle: Further progress towards Hadw... • 20Sept11 Tutte Further progress towards Ha... • What is...the Kuratowski-Wagner theorem?