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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.
3
votes
1
answer
143
views
Broken line that can go in specific directions: can it end up on its starting point?
Say you have a 2D broken line you move along, but only some directions are allowed (I give you the angles relative to the usual cartesian plane):
(Up-Left): $]\pi, \dfrac{\pi}{2}[$
(Down-Left): $] …
2
votes
2
answers
122
views
Odd partition with extra properties
Can such a set $A=$ {$a_1,.. a_k$} exist, such that:
$\sum_i a_i = 1$ and $a_i $ are rational positive numbers
$k$ is and odd number, and is at least $3$.
We can partition $A$ in two parts of value …