Question On Graphs

O

oke

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Aug 2, 2022
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I am trying to solve the following research problem:
Let G be a bounded degree 6 graph with chromatic number 3.
Let W5 be the Wheel graph on 5 vertices.
Is the graph union of G and W5 three colorable?

Can anyone provide a hint/direction so I can make some progress?
 
By "graph union" do you mean a disjoint one? If this is the case then isn't a disjoint union 3-colorable if each component is a 3-colorable graph?
 
oke said:
I am trying to solve the following research problem:
Let G be a bounded degree 6 graph with chromatic number 3.
Let W5 be the Wheel graph on 5 vertices.
Is the graph union of G and W5 three colorable?

Can anyone provide a hint/direction so I can make some progress?
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