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Results tagged with graph-theory
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user 11260
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.
55
votes
Accepted
What are good mathematical models for spider webs?
In response to the second question (which I interpret as asking for math models of spider webs as they appear in Nature): There exist several distinct types of spider webs. The most common type, the o …
- 188k
34
votes
How to find Erdős' treasure trove?
Paul Erdős's notes on Egyptian fractions are with Ronald Graham, who has reproduced some of them in Paul Erdős and Egyptian Fractions. Graham mentions one unfinished manuscript in which "it is shown t …
- 188k
29
votes
Accepted
Who is M. Meyniel?
You can be quite sure that M. Meyniel means "Monsieur Meyniel" (a common usage in French).
Here is what I think is definite proof that M. Meyniel is H. Meyniel: The acknowledgement of the 1973 paper b …
- 188k
23
votes
Hermann Weyl's work on combinatorial topology and Kirchhoff's current law in Spanish
It turns out that Beno Eckmann actually asked Hermann Weyl why he published this work in Spanish, as described here and here. The answer is remarkable and unexpected (and apparently does not involve h …
- 188k
14
votes
Accepted
Proving Hall's marriage theorem using Sperner's lemma
Penny Haxell's 2011 paper On Forming Committees in the American Mathematical Monthly explicitly uses Sperner's lemma to prove Hall's theorem for bipartite graphs (see theorem 4.1 and 4.2).
- 188k
12
votes
An intelligent ant living on a torus or sphere – Does it have a universal way to find out?
I presume the OP has in mind the topological distinction between a sphere and a torus, so the method should apply to deformed surfaces. A meaningful/universally valid method for this purpose must incl …
- 188k
11
votes
Accepted
Intuition of the energy of a graph
The name "energy" only makes physical sense for a bipartite graph, where the eigenvalues of the adjacency matrix come in pairs $\pm\lambda$. If graph represents a molecule, the adjacency matrix is the …
- 188k
10
votes
Accepted
Searching for an early, highly theoretical, even philosophical, math paper on models or smal...
Stanley Milgram, The Small World Problem, Psychology Today 2, 60 (1967)
seems to fit the bill: +50 years old, "kind of philosophical", and yes, iconic -- cited more than 9,000 times. There are a few r …
- 188k
10
votes
regular graphs with the smallest eigenvalue -2?
Connected regular graphs with smallest eigenvalue at least $−2$ are either a line graph, a cocktail party graph, or the number of vertices is at most 28.
P. J. Cameron, J. M. Goethals, J. J. Seidel a …
- 188k
10
votes
How to effectively search Internet for graphs not for function graphs?
Use Google Scholar instead of plain Google; I simply entered graphs and pretty much all the items returned by Google Scholar refer to graphs in the mathematical context.
It also suggests helpful speci …
- 188k
9
votes
Accepted
Has Plummer's open problem on the cyclic connectivity of planar graphs been solved?
Yes, it has been solved.
In 1989 Borodin proved that the maximum cyclic edge connectivity of a 5-connected planar graph is at most 11, improving on Plummer's upper bound of 13. The 11 bound is tight [ …
- 188k
8
votes
Accepted
Can the graph removal lemma be proved directly from the triangle removal lemma?
A proof of the Graph Removal Lemma that avoids using the regularity lemma can be found in A new proof of the graph removal lemma (2010). For an explanation why a direct proof of the Graph Removal Lemm …
- 188k
8
votes
Origin of the banana graph
These diagrams come by different names: "banana", "water melon", "basket ball". An early reference is M. Creutz - Feynman rules for lattice gauge theory, Rev. Mod. Phys. 50, 561–571 (1978). A more re …
- 188k
8
votes
Accepted
Evans conjecture for symmetric latin squares
No, when it comes to symmetric latin squares it is no longer true that as many as $n-1$ cells can be prescribed unconditionally. This is explained in the Ph.D. thesis of Matthew Henderson.
The key po …
- 188k
7
votes
Accepted
exact definition of Fiedler vector
The concept of a Fiedler vector is defined for graphs that consist of one single connected component. Since the number of zero eigenvalues counts the number of connected components, the second largest …
- 188k