1. B

    Complex domain coloring - a form of art

    Hello all, I hope you guys don't mind a little bit of self-promotion, but I recently introduced an advanced complex function plotting feature to Grapher Pro for Android. In short, I would like to share with you the fact that a myriad of undiscovered opportunities exist here, not just for...
  2. L

    graph coloring

    How many ways I can color these graphs using 3, 4 and 5 palette of colors?
  3. L

    graph coloring

    Any idea how I can do combinatorial proof for graph coloring in the question?
  4. U

    Algorithm that may solve coloring problem

    I have a sudo code that is supposed to try to solve a minimum coloring on a graph. And the question is: Does this code solve this minimum coloring problem to any given graph? Code: for (v = v0; v < vn; v++) v >color = 1; k = 0; do { flag = 0; k++; for...
  5. K

    Edge coloring of the cube

    I didn't know exactly which forum branch to choose for this problem: We have a cube and we are coloring its edges. There are three colors available. We say that the two colorings are the same if one can obtain a second by turning cube and permuting colors. Find the number of different...
  6. C

    Coloring problem

    Hello! I solved a problem, but I can't prove it with induction. Here it is the problem: Draw n arbitrary circles in the plane and suppose that the obtained image is a map. Prove that we can color this map with 2 colors such as two regions having a common border have different colors. The...
  7. N

    Graph theory : coloring edges

    Hello, here is a "funny" problem. This is not homework and I don't need urgent answer. Consider an integer n>1 and n colors. Take a complete graph and color the edges such that for any three distinct vertices, one color occurs exactly twice. What is the maximal possible number of vertices ...
  8. R

    digraph: cycle of an even length and coloring the vertices

    Prove that the following two conditions for a strongly connected directed graph G are equivalent: 1. G contains a directed cycle of an even length. 2. The vertices of G can be colored by 2 colors (each vertex receives one color) in such a way that for each vertex u there exists a directed edge...