A small Chromatic number thing for a redditor

English_to_French_Actors.sagews

︠from sage.graphs.graph_coloring import vertex_coloring

# This is the list of English actors in the order they appear
english_actor_sequence = [
     1,  2,  3,  1,  5,  4,  2,  6,  1,  3, 
     2,  9,  6,  3, 10, 11,  3,  2, 12,  1, 
    13, 14, 12,  2,  7,  6,  1, 13, 11,  5, 
    13, 15,  7, 12, 10, 16, 17,  2,  3,  6, 
    12, 17, 15,  5,  4, 13,  2,  7,  1, 14, 
    10, 15,  9,  4,  2]

# Two French actors cannot take roles of English actors in consecutive scenes
actor_pairs = [(english_actor_sequence[i],english_actor_sequence[i+1]) for i in range(len(english_actor_sequence) - 1)]

# Create a graph where the English actors are nodes, the edges are whether two English actors are in consecutive scenes
# Multiedges are not needed
scene_graph = Graph(actor_pairs, multiedges=False)

# Show the graph before colouring
scene_graph.graphplot(layout='circular').show(figsize=[6,6])

# Display the info
print 'You need %d French actors.' % vertex_coloring(scene_graph, value_only=True)
print 'These are the English roles the French actors will take: '
for i in range(vertex_coloring(scene_graph, value_only=True)):
    print 'French actor %d will play the parts: ' % (i+1)
    print vertex_coloring(scene_graph)[i]

#Show the coloured graph
scene_graph.graphplot(layout='circular', partition=vertex_coloring(scene_graph)).show(figsize=[6,6])

Code for this comment:

https://www.reddit.com/r/math/comments/82yzln/if_i_had_a_sequence_of_16_actors_some_recurring/

Here's the output:

You need 5 French actors.
These are the English roles the French actors will take: 
French actor 1 will play the parts: 
    [6, 10, 13, 17]
French actor 2 will play the parts: 
    [7, 3, 5, 16, 14, 9]
French actor 3 will play the parts: 
    [2, 15, 11]
French actor 4 will play the parts: 
    [12, 4]
French actor 5 will play the parts: 
    [1]

Here's the picture:

https://cocalc.com/blobs//home/user/.sage/temp/project-fbeb3d9c-3251-4e88-9e27-82a1c37642e1/270/tmp_uijHct.svg?uuid=3877e5a6-2b20-41df-b57d-9d862c4d7394