Edge Colorings and Chromatic Index of Graphs | Graph Theory

We introduce edge colorings of graphs and the edge chromatic number of graphs, also called the chromatic index. We'll talk about k-colorings/k-edge colorings, minimum edge colorings, edge colourings as matchings, edge colourings as functions, and see examples and non-examples of edge colorings. #GraphTheory
An edge coloring of a graph (sometimes proper edge coloring) is an assignment of colors to the edges of a graph such that adjacent edges are colored differently.
What are Adjacent Edges? • What are Adjacent Edge...
Matchings: • Matchings, Perfect Mat...
Vertex Colorings and Chromatic Numbers: • Vertex Colorings and t...
Graph Theory playlist: • Graph Theory
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[@WrathofMath]

Check out my lesson on vertex coloring! th-cam.com/video/3VeQhNF5-rE/w-d-xo.html

[@aashsyed1277]

Nice explanation! 👍

[@quezcatol]

was waiting for this, thanks!

[@WrathofMath]

My pleasure! Thanks for watching!

[@aashsyed1277]

Awesome 😎

[@alejandrorz6577]

Just waiting for the Vizing's theorem video, the proof of that theorem its really neat.

[@visheshjindal9853]

++

[@PunmasterSTP]

I bet it's gonna be a real Vizinger!

[@0peter897]

Nice explanation, thank you! One note: Vizing's theorem can only be used to simple graphs. (I failed my midterm, because I forgot about this :c )

[@ponnu1500]

Very useful video.. Thankyou

[@WrathofMath]

Glad to hear it, thanks for watching!

[@rajendragoudar2961]

Nenga suriya fan ah?

[@ponnu1500]

@@rajendragoudar2961 yes.. Surya fan

[@vonage_sasb9356]

Hello,
Do any one know answer for "Does there exist a 3-edge colourable graph with 10 vertices and 20 edges ?"

[@chaotischekreativitat9391]

Sounds like an exercise question 😂
Hint: Think about the degrees of those vertices that are possible under these circumstances.

[@neutronology5524]

nice im using it in class rn

[@WrathofMath]

Thank you for watching, glad it helped!

[@PunmasterSTP]

That's cool. How'd the rest of your class go?

[@janmarjagolina1235]

Is empty graph has 0 chromatic index?

[@tshwareloshabalala8394]

Hello. Yes I suppose, since there are no edges to color.

[@dhe1782]

How to proof that the crossing number of K6 is 3. Thanks!!

[@PunmasterSTP]

Oh man, another edgy lecture...

[@vonage_sasb9356]

Hello,
Do any one know answer for "Does there exist a 3-edge colourable graph with 10 vertices and 20 edges ?"

[@umarmurtala5572]

From my little understanding, I don't think it exists, since an graph graph can't be 3 edge colorable

[@vonage_sasb9356]

@@umarmurtala5572 Yes you are correct