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Graph theory and combinatorics

Anonymous Fri 27 Dec 17:10:25 2019 No.11257462 View Reply Original Report

Quoted By: >>11257506 >>11257556 >>11257607

Why are graph theory and combinatorics so closely related? What is the relationship between the two? It seems like every other book I find online for graph theory is titled “combinatorics and graph theory”.

Anonymous

Anonymous Fri 27 Dec 2019 17:33:28 No.11257492 Report

Quoted By:

bump

Anonymous

Anonymous Fri 27 Dec 2019 17:39:19 No.11257506 Report

Quoted By:

>>11257462
the theorems in graph theory that people care about involve counting. Combinatorics is the study of counting. Hence the connection.

Anonymous

Anonymous Fri 27 Dec 2019 17:40:41 No.11257508 Report

Quoted By:

because graphs are combinations of edges i guess...

Anonymous

Anonymous Fri 27 Dec 2019 18:06:15 No.11257549 Report

Quoted By: >>11257602

Simply because people usually only work on problems of finite and countable graphs.

Anonymous

Anonymous Fri 27 Dec 2019 18:09:48 No.11257556 Report

Quoted By: >>11257570

>>11257462
every combinatorics problem can be expressed as a graph

Anonymous

Anonymous Fri 27 Dec 2019 18:17:10 No.11257570 Report

Quoted By: >>11257601

>>11257556
Thats interesting.

I bought a graph theory book the other day and one of the questions was a straight combinatorics question, I was curious why it was in the graph theory book.

The question was how many chess matches there would be if 5 players play one another only once.
The solution could also be found by counting the edges of a complete graph with 5 vertices.
It was interesting.

Is it intuitive to express every combinatorics question as a graph theory problem?

Anonymous

Anonymous Fri 27 Dec 2019 18:29:16 No.11257601 Report

Quoted By: >>11257610

>>11257570
yes and no. later down the road you will realize that using graph theoretic methods is somewhat limiting but this is where it gets interesting. im currently a phd student at an R1 school for pure math, and it gets quite neat later on. as a current side project, we are using graph theory and PDE's to model combinatorial problems.

Anonymous

Anonymous Fri 27 Dec 2019 18:29:32 No.11257602 Report

Quoted By:

>>11257549
That makes sense, however, wouldn’t combinatorics then be a choice pairing for any field concerned with that which is finite and countable?
It seems to me that there is something more fundamental to graph theory and combinatorics that makes them pair together so well.

Anonymous

Anonymous Fri 27 Dec 2019 18:32:31 No.11257607 Report

Quoted By:

>>11257462

> why are graph theory and combinatorics so closely related

By definition, graph theory $\subseteq$ combinatorics

Anonymous

Anonymous Fri 27 Dec 2019 18:33:05 No.11257610 Report

Quoted By:

>>11257601
That sounds very cool.
Unfortunately, I’m a computer science student and my only exposure to combinatorics and graph theory were through mandatory discrete math courses. There aren’t vast prospects in my foreseeable future in further mathematical development for me, it seems.

I purchased a graph theory book to read for leisure, and have been enjoying it thus far. It’s only a shame that I will most likely not be learning anymore about pure math in a rigorous setting like a classroom anymore.

Are there any texts on combinatorics or graph theory that you would recommend?

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