# Face Chromatic Number of A Graph

by Cuttlas
Tags: chromatic, face, graph, number
 P: 15 Hi What is the face chromatic number for the Graph Below? Thank You
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,682 Four.
 P: 15 Why is it 4? Look at image below, the face chromatic number is 2, so it should not be 4. Could u please explain for me how did u get 4?
P: 1,403
Face Chromatic Number of A Graph

 Quote by Cuttlas Why is it 4? Look at image below, the face chromatic number is 2, so it should not be 4. Could u please explain for me how did u get 4?
It can't be the chromatic number of the vertices either, because that's equal to 3.

The chromatic number of a map with one ore more closed loops as borders is always 2. You get a bipartite graph with all the nodes that are separated from the outside with an odd number of borders on one side, and those separated by an even number of borders on the other side.
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P: 15
 Quote by willem2 It can't be the chromatic number of the vertices either, because that's equal to 3.
If It can not be 2, then How I painted the Graph's Faces with only two colors? As you can see Faces in painted graph with different colors is not Adjacent with each other. So it means I did the painting correctly. But I think I'm mistaking. Could u please upload the painted graph which u think it is right?
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P: 9,917
 Quote by Cuttlas If It can not be 2, then How I painted the Graph's Faces with only two colors? As you can see Faces in painted graph with different colors is not Adjacent with each other. So it means I did the painting correctly. But I think I'm mistaking. Could u please upload the painted graph which u think it is right?
I think willem2 was agreeing with you that the face chromatic number is not 4.
P: 15
 Quote by haruspex I think willem2 was agreeing with you that the face chromatic number is not 4.
:) Yes, it seems your right. Then Does it mean I'm right? The Face chromatic number is 2 or 3?
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