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Graph coloring problem? - Mathematics Stack Exchange
Is there a problem of graph coloring (and what is its name) defined as: If a node is colored with one color all adjacent nodes will have the same color. What is minimal number of colors to do that?...
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How to prove that the 4-coloring problem is NP-complete
Since every color is connected to the new vertex, this vertex needs a new 4th color.Nevertheless, this 4 colored Graph can only be colored correctly, if the original 3 colored Graph is colored correctly. Therefor I reduced the 3 colore problem to a 4 color problem. Does this make sense?
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How is the graph coloring problem NP-Complete?
The Graph Coloring decision problem is np-complete, i.e, asking for existence of a coloring with less than 'q' colors, as given a coloring , it can be easily checked in polynomial time, whether or not it uses less than 'q' colors. On the other hand the Graph Coloring Optimisation problem, which aims to find the coloring with minimum colors is np-hard, because even if you are given a coloring ...
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combinatorics - Why do greedy coloring algorithms mess up ...
It is a well-known fact that, for a graph, the greedy coloring algorithm does not always return the most optimal coloring. That is, it strongly depends on the ordering of the vertices as they are c...
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coloring - Using the reduction of 3-SAT to 3-COLOR, explain why ...
What I'm wondering is why solving those instances G resulting from reduction of 3-SAT to 3-COLOR is the same as solving all instances of 3-COLOR. It's not. The point is to be able to solve just the 3-SAT examples. If the 3-COLOR problem is about whether a graph with structure similar to G is 3-colorable, then this approach works. But clearly it isn't. Absolutely. But the point of the proof is ...
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graph theory - Coloring problem with limited number of each colors ...
9 I’m investigating graph coloring problem. But I cannot find any solution about the problem with limited number of each colors. I mean, Suppose three colors (green, red, blue) and a graph, we start to color each vertex, but (If green color’s limit is 3) we cannot color as green after we already used green 3 times.
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Graph colouring problem: 6 and 5 colouring theorems and algorithms
Do this for all verices. Now the 5 - colour theorem: Every planar graph is 5-colorable (a planar graph is a graph in which no two edges intersect). My professor told me that this doesn't apply for a 5 - colouring, due to the fact that each vertex can has 5 neighbors which use the 5 given colors and told me to go for something else.
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coloring - Why problem of Graph colouring is NP-Hard? - Mathematics ...
I am studying graph coloring and trying to find why graph coloring is NP-Hard. Please share your thoughts or share any resources related to this.Thank you in Advance.
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discrete mathematics - Why finding chromatic number is NP-Hard ...
Do you know what NP-Hard means in terms of theoretical computer science ? It essentially means that any problem in NP can be transformed so it becomes the problem of finding the chromatic number of a graph. And can you define vertex coloring ? As far as I know, it's the same thing.
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Complement of Graph Coloring Problem - Mathematics Stack Exchange
3 Not if you don’t impose some assumption like the coloring being minimal or something. Color the graph $\bullet \;\;\bullet$ with two different colors. The complement is $\bullet - \bullet$, which has an edge, although the nodes had different colors. Even when imposing minimality the claim remains false.