Graph_coloring

Assigning 4-chromatic or 5-chromatic labels to a planar graph vertices, such that there's no 2 adjascent vertices that have the same colour.

• NetworkX

Algorithm used for 4-coloring:

 ```
 init waiting_list <- first_node
 init visited list
 
 While there's items in the waiting_list, do:
     refresh options for colors
     current_node = first on the waiting_list 
     (current_node gets to be popep out from waiting list)
     add all neighbors to waiting list, if they are not there and they are not listed in visited
     color current_node:
          remove curent_node's neighbors' colors (if they exist) from the options
          color with the first option in the list
     maked the current_node as visited
 Plot graph
 ```

• use fourCC.py to plot or make gif -> custom input of parameters

Algorithm used for 5-coloring

     dictionary -> adjacency matrix -> graph
     check planarity
     color nodes such that every 2 adjacent nodes have different labels -> it will probably clash around the 5-degree vertice
     order the neighbors of 5-degree vertice in clockwise order
     swap color between vertice 1 and 3 if they are not connected, otherwise swap colours of v2 and v4.
     plot the graph using the right color labels

• for a static plot, use coloring2 function from drawing.py; for gif, use gifmaker.py from fiveCC
• theory and explanation for 5-coloring in the notebook
• didn't work for randomly generated graphs -> neighbors of 5d node should connected for it to work (?)