Assignment. Your goal for today is to refine the conjecture you decided on during your last class meeting. Some things to consider:
- Specificity: The conjecture should be stated clearly. It should include all information necessary to be understood by someone who is familiar with graph theory terms (vertex, edges, paths) and familiar with the assignment (walking tours). A reader should be able to tell from the statement whether a conjecture applies to a given drawing or not.
- Generality: Your conjecture should apply to more than just a single specific graph (it can apply to a collection of similar graphs, for example, as long as you describe exactly what types of graphs you are considering).
- Drawing: You can create a drawing to accompany your conjecture, but your conjecture should be understandable without the picture.
- You can revise your conjecture as a group if you wish – but try to come up with something similar.
- You can add additional clarification to your conjecture.
- You can extend your conjecture to include more types of graphs.
Group 2 Conjecture : Deborah, Josiel, Sanaya, Irania
(Updated, Official Conjecture)
It is impossible to solve a graph that has 3 or more vertices with degree 1. If you were to start from the inside (where the inside is considered a vertices with degree 2 or more) then there will be more edges that aren’t covered.
*I hope this makes sense lol*
group 3:
Abdelmajid
Zha Mei
Xiong lin
CONJECTURE description in words:
To start the conjecture draw a circle containing a vertex O( origin O) and edge( radius) than draw an equilateral triangle outside it such that its edge midpoints touch the circle after that draw another circle outside the previous triangle and has the same origin O. to complete the conjecture draw another equilateral triangle such that its edge midpoints touch the previous circle and its base parallel to previous triangle, and last, add another circle outside the triangle such that it touches the 3 vertices of the last triangle.
http://sketchtoy.com/66091618 this is the conjecture link
CONJECTURE:
Is it possible to find a walking tour staring from the vertex 0( origin of small circle) and get to the vertex A ( point in the big circle) passing by all the edges once and not repeating any edge.
THEORY:
If the conjecture is true for this particulate conjecture described above, then is it true if we add as many triangles and circles( respecting the same pattern) as we want.
Group 4
Daniela
Ryan
Yuyu
Fuzail
If you have a shape (Polygon), and there is a vertex in the center, and we connect all the vertices of the polygon to the center vertex, then no walking tour can be made.
http://sketchtoy.com/66091858
Group 1
Any 2 Polygons joined by 1 edge is solvable. However, any n > 2 polygons joined by m edges is not solvable, where n and m are integers.
http://sketchtoy.com/66109104