All Questions

From the well-known Nine dots problem, we know that we need a polygonal chain with at least $4$ edges to connect the $9$ points of the planar grid $G_{3,2}:=\{\{0, 1, 2\} \times \{0, 1, 2\}\} \subset \...

Let $T_{\mathrm{MIN}}$ and $T_{\mathrm{MAX}}$ denote the shortest, resp. longest Hamilton cycle through a set of $n=2k+1$ points. Let further $S_{\mathrm{MIN}}$ and $S_{\mathrm{MAX}}$ be the "...

A salesman is employed by a large corporation. He has a $n$ cities to visit, connected by roads, forming a graph. But as travel takes a lot of time, he has to pick hotels between visits. He cannot ...

let $\mathcal{P}$ be a finite set of points in the euclidean plane in general position, and let $$\lbrace p_A,p_B,p_C,p_D\rbrace: \ \|p_C-p_A\|+\|p_D-p_B\|\ \gt \|p_i-p_h\|+\|p_k-p_j\|\quad\forall\ \...

I have an array of points with their coordinates X and Y. Each point represents a bus stop. I need to sort the points in a sequence by giving them sequence numbers, so that the path from the first to ...