# planar

1. ### Planar Inequalities

My goal here is to figure out a routine to determine if a point lies within a certain distance of a plane. I understand the standard form of planes (ax+by+cz=d) and that the equation itself represents the normal vector, but what I'm having trouble with is d. I know you can test a point on a...
2. ### Curvature and solving a limit for planar curves

Hey guys, I've been stuck on this limit for a while. I tried representing the curve in a basis with the unit tangent and the principal normal. I didn't really know what to do from there.
3. ### Finding planar curves with constant curvature

Hey guys, I'm completely stuck on the following question: Find all planar curves with constant curvature When K = 0, it is simply a line. That is easily shown by equating r'(t) = r'(0) and integrating both sides. This is not applicable when curvature is non-zero.
4. ### Planar line translation and rotations...

We have planar lines in the form of $X=tP+sQ$, where $P$ and $Q$ are two fixed different points and $s,$ $t$ are varying reals satisfying $s+t=1$. We need to find the formula for the images of the line $X=tP+sQ$ in the following three cases: 1. Under the translation by a vector B. 2. Under...
5. ### Complement graph not planar

Hello, I have the following question: Let G be a simple graph with 2 connected components. Each component has at least 3 edges. Prove that G's complement graph is not planar. Now what I thought would make sense is that all the edges in the complement graph cross each other so it can't be...
6. ### Possible to find unbounded face cycles based on planar embeddings? [Graph]

Given a set of face cycles computed from a planar embedding (consisting of a clockwise ordered adjacency list for each vertex in a connected graph component), is it possible to determine the unbounded face? Visually it's easy to confirm since the unbounded cycle will be traversed on the...
7. ### Question related to Euler's planar graph formula

Hi, Our teacher asked us this question : "Prove that a simple, connected, bipartite and planar graph verifies : n \ge f + 2. From this, find a proof that K_{3,3} is not planar." Proving that isn't hard, but a friend told me that for n=2 (2 vertex), this fails ! Euler's formula : f = e - v + 2...
8. ### Planar graph drawing

I am tasked with drawing a planar graph with no loops or multiple edges, and every node has to have at least 5 edges coming out of it. Nothing seems to work, any help?
9. ### question regarding connected planar graph

Let G be a connected planar graph with n vertices (where n >= 3), e edges (where e >= 3), r regions, and no cycle of length 3 or less. Show that (e =< 2n - 4) I've tried to use the handshake formula and the eular's formula to solve this problem, but it doesn't seems like I am doing the right...
10. ### Planar graph

Hi I have this graph now i should check if this graph can be planar. v - number of vertices e - number of edges f - number of faces So it's hold the theorem "If v ≥ 3 then e ≤ 3v − 6 " v = 9, e = 15 15 ≤ 21 and should hold v - e + f = 2 from here f = 2 - v + e = 2 - 9 + 15 = 8 so f = 8 now...
11. ### Every vertex in a 5-chroma planar graph must have degree >=5. WHY?!

I keep reading that Kempe has proven that every vertex in a 5-chroma planar graph must have degree >= 5, but nowhere can I find this proof. Could someone please explain the proof or point me in the right direction? Many thanks in advance, Katie
12. ### Proof about closed orbits of a planar system

"Prove that a closed orbit of a planar system meets a local section in at most one point." Isn't this true by the Poincare-Bendixson Theorem? How do I prove this rigorously?
13. ### Planar Graphs

If G is a simple planar graph, does G contain a vertex of degree at most four? Prove or provide a counter example. Thanks!
14. ### Maximal 4-regular Planar Graph

I've been asked to prove that there is only one 4-regular planar graph. We've used Euler's formula and the fact that the size must equal 3n - 6 to show that the order must be 6. Could someone walk me through it? Thanks.
15. ### Planar intersections

Hello all, i wonder if you can help me with a problem im having. I have a disc and three planes (representing a road, building and roof). For this problem, the disc can be considered a plane. http://i3.photobucket.com/albums/y60/con20or/Fig1.png I know the orientation of each of the planes...
16. ### Graph theory boyer-myrvold planarity test thinks non-planar graph is planar

I am trying to find a way to identify if a graph is planar or not. Using the boost graph library there is the boyer-myrvold algorithm. This seems to work except it finds some non-planar graphs are planar. This is because edges are stretched out of position. For example see the three graphs...
17. ### Planar graphs. Hint please :)

Is there a connected planar (simple) graph such that: (a) each vertex has degree 4? Havn't done decision maths in a while and googles not much help.(or maybe im not looking very well!) Just need a hint really if you can. :). Im tempted to say there is not...but im not sure if im meant to use...
18. ### Planar intersection

so I have a question I cannot answer in my calculus/vectors course, and it's driving me insane. if someone could just tell me how to find k i would be forever grateful. 'Find the value of k such that the three planes will always intersect in a point, then find the point of intersection.'...
19. ### Planar graphs

Show that any graph having five or fewer vertices and a vertex of degree 2 is planar. I don't understand the question. Are they saying 5 or fewer vertices AND 1 vertex with a degree of 2? 5 or fewer vertices with degrees of 2? Is it asking something else? If the first, could I put 3...
20. ### planar curve

show that the curve: γ(t)=[(1+t²)/t),t+1,(1-t)/t)] is planar