Register to reply

Face Chromatic Number of A Graph

by Cuttlas
Tags: chromatic, face, graph, number
Share this thread:
Cuttlas
#1
Sep1-14, 06:54 AM
P: 15
Hi

What is the face chromatic number for the Graph Below?



Thank You
Phys.Org News Partner Science news on Phys.org
Wearable 4MM jetpack tested on speed, agility for runners (w/ Video)
How did evolution optimize circadian clocks?
Corn spots: Study finds important genes in defense response
HallsofIvy
#2
Sep1-14, 08:44 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,682
Four.
Cuttlas
#3
Sep1-14, 10:03 AM
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?


willem2
#4
Sep1-14, 10:45 AM
P: 1,403
Face Chromatic Number of A Graph

Quote Quote by Cuttlas View Post
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.
Attached Thumbnails
chrnum.png  
Cuttlas
#5
Sep1-14, 12:27 PM
P: 15
Quote Quote by willem2 View Post
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?
haruspex
#6
Sep1-14, 04:47 PM
Homework
Sci Advisor
HW Helper
Thanks
P: 9,917
Quote Quote by Cuttlas View Post
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.
Cuttlas
#7
Sep1-14, 11:04 PM
P: 15
Quote Quote by haruspex View Post
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?
haruspex
#8
Sep2-14, 12:33 AM
Homework
Sci Advisor
HW Helper
Thanks
P: 9,917
Quote Quote by Cuttlas View Post
:) Yes, it seems your right. Then Does it mean I'm right? The Face chromatic number is 2 or 3?
Your own diagram seems to prove it's 2. Why are you unsure?


Register to reply

Related Discussions
Spatial graphs and their chromatic number General Math 12
Minimum number of edges in a graph of order n with chromatic number k Set Theory, Logic, Probability, Statistics 1
Funny Face Graph using Parent Functions Calculus & Beyond Homework 1
Chromatic number of the n-cube General Math 3
Chromatic number of 3-space General Math 0