Re: Three quesition about graph coloring

I am sorry about that I forgot that
I cannot use some special symbol here
so I rewrite the first article.

A ^S^ B:= the set of intersection for set A and set B
A vSv B:= the set of union for set A and set B
X(G):= chromatic number of simple graph G


To define the function CLRS: {graphs} -> { sets of function(s)}
s.t. G |-> {f | f:V(G)->{1,2,...,X(G)} is proper coloring}


Suppose G, H be any simple graph...
Is "CLRS(G)=CLRS(H) <-> G is isomophic to H " ?
Is always exist simple graph F s.t. CLRS(F)=CLRS(G) ^S^ CLRS(H)?
Is always exist simple graph F s.t. CLRS(F)=CLRS(G) vSv CLRS(H)?


At first, I never know the discussion for set of coloring.
I just get the idea, but I'm not ensure whether it's good or bad.
I just get a new thinking about this.


Is any book ever talk about something like this?


Thank you.

.

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