http://www.bing.com:80/search?q=Graph+Coloring+ProblemSearch resultshttp://www.bing.com:80/s/a/rsslogo.gifhttp://www.bing.com:80/search?q=Graph+Coloring+ProblemCopyright © 2026 Microsoft. All rights reserved. These XML results may not be used, reproduced or transmitted in any manner or for any purpose other than rendering Bing results within an RSS aggregator for your personal, non-commercial use. Any other use of these results requires express written permission from Microsoft Corporation. By accessing this web page or using these results in any manner whatsoever, you agree to be bound by the foregoing restrictions.https://math.stackexchange.com/questions/125136/how-is-the-graph-coloring-problem-np-completeThe 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 ...Sun, 19 Apr 2026 05:11:00 GMThttps://math.stackexchange.com/questions/3284838/graph-coloring-problemIs 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?...Sat, 18 Apr 2026 23:42:00 GMThttps://math.stackexchange.com/questions/3149179/using-the-reduction-of-3-sat-to-3-color-explain-why-complexity-proofs-by-reductWhat 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 ...Sat, 18 Apr 2026 20:14:00 GMThttps://math.stackexchange.com/questions/4405296/why-problem-of-graph-colouring-is-np-hardI 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.Fri, 17 Apr 2026 05:35:00 GMThttps://math.stackexchange.com/questions/4449919/why-do-greedy-coloring-algorithms-mess-upIt 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...Fri, 17 Apr 2026 10:00:00 GMThttps://math.stackexchange.com/questions/3272231/proving-np-completeness-for-a-problem-is-a-generalization-of-a-known-np-completeThe new problem is completely equivalent to the original one. This is a polytime reduction, and so since GCP is NP-hard, so is LCP. In order to show that LCP is actually NP-complete, you need to show that it is in NP. Here the reduction is of no help, and you have to prove it directly.Thu, 09 Apr 2026 20:03:00 GMThttps://math.stackexchange.com/questions/385145/map-coloring-problem1 Historically, the map-coloring problem arose from (believe it or not) actually coloring maps. There, if two countries share a common border that is a whole line or curve, then giving them the same color would make the map harder to read; the border would not be so clearly visible as if you used different colors.Sat, 18 Apr 2026 12:43:00 GMThttps://math.stackexchange.com/questions/4143003/complement-of-graph-coloring-problem3 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.Thu, 16 Apr 2026 07:24:00 GMThttps://math.stackexchange.com/questions/2548145/representing-graph-colouring-as-a-propositional-formulaLet n be the number of elements in V . A ”graph coloring” signs a color to each vertex, such that if two vertices are connected, then they have a different color. A graph coloring using at most k colors is called a k-coloring. The Graph Coloring Problem asks whether a k-coloring for G exists."Fri, 27 Mar 2026 17:27:00 GMThttps://math.stackexchange.com/questions/3241339/how-to-prove-that-the-4-coloring-problem-is-np-completeSince 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?Fri, 17 Apr 2026 01:53:00 GMT