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Jan
25
answered How to find irrational numbers between rationals. (And is my method correct?)
Jan
14
comment Calculate the resistance between 2 adjacent nodes on a shape using graph theory
There are many connections between electrical flows and graph theory. Some search terms are: "electrical flow laplacian", "electrical graph theory", "electrical circuit networks graph".
Dec
23
comment Simplest algorithm for edge coloring of a dodecahedron?
Why don't you search for a picture and copy its pattern? If you definetely need a method, you could devise a hamiltonain cycle (see here) and then color it with two colors, and all the rest with the third color.
Dec
21
comment What are some concrete examples of how Graph Theory can be applied to Finite State Machines?
I think that the second part of your question is too broad. With regard to automatons, the transition function can be represented as a graph, and anything you do to it in that form could be considered graph theory, e.g. checking reachibility or some minimization algorithms.
Dec
14
awarded  Self-Learner
Nov
29
comment Hexagon tesselations
Although impossibility proofs are hard in general, in this case there are only a few configurations to check (any configuration of 4 hexagons has at least 16 vertices).
Nov
24
answered Understand it or burn
Nov
12
comment Graph Puzzle with labels
You tagged this 'recreational math', so I won't give away all the details. I've already posted too much!
Nov
12
awarded  Popular Question
Nov
11
answered Bipartite graphs, maximum size matchings, Hall's condition
Nov
10
answered Graph Puzzle with labels
Nov
10
comment Show that if G(U, W) is a bipartite graph such that min u∈U degree(u) ≥ max w∈W degree(w), then G has a matching of size |U|.
@Jonathan Yep ;-)
Nov
10
answered Show that if G(U, W) is a bipartite graph such that min u∈U degree(u) ≥ max w∈W degree(w), then G has a matching of size |U|.
Oct
29
comment Set builder notation: Colon or Vertical Line
In such cases I use different sizes of the vertical bar, e.g. $$\Big\{x\in X \ \Big|\ \big||x|-|y_0|\big| < \varepsilon \Big\}.$$
Oct
29
awarded  Announcer
Oct
24
comment Cheapest subgraph of a tree that contains any $k$ vertices?
Use Prim's algorithm and stop at the right moment.
Oct
23
comment Simple Proof in Pure Mathematics that has applicability
On the other hand, there are a few places where you can see a glimpse of pure math, like the matching theory I mentioned, or group testing which uses coding theory. If you are not familiar, the latter is, in my opinion, quite illuminating.
Oct
23
comment Simple Proof in Pure Mathematics that has applicability
@hariq Unfortunately, any example that I know of at the level of simplicity you require is trivial, and wouldn't be taken seriously. The even/odd numbers can be thought of as "pure math" in the context of group $\mathbb{Z}_2$, but this not even a tip of an iceberg. One of the reasons why people considered pure math useless, is that the useful bits are often a bit more complicated and we needed time to discover their applications.
Oct
12
comment Prove that this graph is nonplanar
For simple graphs it is quite easy to see (e.g. by eyeballing) if a graph is planar when it is planar. Thus, I tried to remove edges one by one without breaking non-planarity. While doing that I observed that the graph of crucial edges was not bipartite, so that ruled out $K_{3,3}$. After that, I started with 5 colors in 5 almost random vertices and colored their neighbors to form $K_5$. The diagram was done in Inksacpe.
Oct
12
answered Prove that this graph is nonplanar