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Results tagged with graph-theory
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user 156936
Questions about the branch of combinatorics called graph theory (not to be used for questions concerning the graph of a function). This tag can be further specialized via using it in combination with more specialized tags such as extremal-graph-theory, spectral-graph-theory, algebraic-graph-theory, topological-graph-theory, random-graphs, graph-colorings and several others.
150
votes
Accepted
Issue UPDATE: in graph theory, different definitions of edge crossing numbers - impact on ap...
$\DeclareMathOperator\cr{cr}\DeclareMathOperator\pcr{pcr}$For the pair crossing number $\pcr(G)$, the short answer is yes the crossing lemma holds for drawings on the sphere, but it is not known wheth …
- 6,937
30
votes
Accepted
Why did Robertson and Seymour call their breakthrough result a "red herring"?
Seymour and Robertson have indeed said that, and in fact they wrote that in their 2003 article in which they published the graph structure theorem.
Here is the quote from Robertson and Seymour „Graph …
- 6,937
30
votes
Issue UPDATE: in graph theory, different definitions of edge crossing numbers - impact on ap...
@user161819 I wanted to make a comment but it got too long, so putting it as an answer. But please take it just as a comment for later, once everything is finished:
If I understand your comment to my …
- 6,937
17
votes
Reference for topological graph theory (research / problem-oriented)
My recommendation, try Lando and Zvonkin (2004): Graphs on Surfaces and Their Applications.
I think it is a great book which applies graphs embedded on surfaces to solving problems from other fields o …
17
votes
Intuitively, what does a graph Laplacian represent?
This is just a long comment, adding to the excellent answers above.
There is a great article from László Lovász "Discrete and Continuous:
Two sides of the same?", written around 2000 (https://web.cs.e …
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15
votes
Accepted
Reference for topological graph theory (research / problem-oriented)
Maybe this is another useful reference for you, now I found the link:
Ralucca Gera, Stephen Hedetniemi, Craig Larson, Teresa W. Haynes (editors) (2018): Graph Theory: Favorite Conjectures and Open Pro …
9
votes
Accepted
Conjecture of van der Holst and Pendavingh related to bound for Colin de Verdière invariant
Kaluza and Tancer have actually proved $\mu(G)\leq\sigma(G)$ in 2019: See their proof in the preprint "Even maps, the Colin de Verdière number, and representations of
graphs" on arxiv. Here is the lin …
- 6,937
5
votes
Accepted
Interpretation around conjugacy classes in group theory
Regarding your first question, I think the comment of Henrik Rüping gives the best answer.
Regarding your second question, I am not sure about a geometric interpretation, but maybe the following persp …
- 6,937
4
votes
Accepted
Hadwiger number of a graph: Question about the original article from 1943
Let me give it a try. As a disclaimer, English is not my mother tongue, so my translation might have linguistic flaws.
First of all, I would say the sentence is hard to translate and it is a bit infor …
- 6,937
3
votes
Sperner's Lemma implies Tucker's Lemma - simple combinatorial proof
Just to close the loop on this. I now found a simple proof that an antipodally symmetric labelling of the boundary always has a valid Sperner coloring (in two dimensions). This means Tucker’s Lemma ac …
- 6,937