What is...the genus of a graph?

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...the genus of a graph? Or: Building bridges.

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://en.wikipedia.org/wiki/Bridge#...

Main discussion.
https://math.stackexchange.com/questi...
https://en.wikipedia.org/wiki/Genus_(...)
https://mathworld.wolfram.com/GraphGe...
https://doi.org/10.1016%2F0196-6774%2...
https://math.stackexchange.com/questi...

Background.
https://en.wikipedia.org/wiki/Graph_e...
https://en.wikipedia.org/wiki/Planar_...
https://mathworld.wolfram.com/PlanarG...
http://oeis.org/A049370
http://oeis.org/A049371
http://oeis.org/A049372
http://oeis.org/A049373
http://oeis.org/A003094
http://oeis.org/A000944
http://oeis.org/A007083
https://en.wikipedia.org/wiki/Kuratow...
https://mathworld.wolfram.com/Kuratow...
https://en.wikipedia.org/wiki/Wagner%...
https://www.theoremoftheday.org/Combi...
https://www.theoremoftheday.org/Combi...
https://en.wikipedia.org/wiki/Complet...
https://en.wikipedia.org/wiki/Three_u...
https://en.wikipedia.org/wiki/Complet...
https://www.fmf.uni-lj.si/~mohar/Book...

Mathematica.
https://demonstrations.wolfram.com/Is...
https://reference.wolfram.com/languag...
https://reference.wolfram.com/languag...

Pictures used.
Pictures from https://www.dtubbenhauer.com/lecture-...
https://alexispenamth350.files.wordpr...
https://i0.wp.com/wwwmathlabo.univ-po...
Picture from https://math.stackexchange.com/questi...
https://www.preceptservices.com.au/wp...

YouTube and co.
What is...the chromatic number of a s... (Shameful self-promotion)
https://en.wikipedia.org/wiki/Planar_...
GTAC 8.4: Fary's Theorem

#graphtheory
#topology
#mathematics