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This is an accepted version of this page This is the latest accepted revision, reviewed on 7 January 2025. Book containing line art, to which the user is intended to add color For other uses, see Coloring Book (disambiguation). Filled-in child's coloring book, Garfield Goose (1953) A coloring book is a type of book containing line art to which people are intended to add color using crayons ...
Print/export Download as PDF ... Pages in category "NP-hard problems" The following 20 pages are in this category, out of 20 total. ... Radio coloring;
Print/export Download as PDF; ... Complete coloring; Connected dominating set; ... This page was last edited on 12 July 2024, ...
Graph coloring is computationally hard. It is NP-complete to decide if a given graph admits a k-coloring for a given k except for the cases k ∈ {0,1,2}. In particular, it is NP-hard to compute the chromatic number. [33] The 3-coloring problem remains NP-complete even on 4-regular planar graphs. [34]
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A simple example of an NP-hard problem is the subset sum problem. Informally, if H is NP-hard, then it is at least as difficult to solve as the problems in NP. However, the opposite direction is not true: some problems are undecidable, and therefore even more difficult to solve than all problems in NP, but they are probably not NP-hard (unless ...
In graphs where every vertex has at most three neighbors, the clique cover remains NP-hard, and there is a constant ρ > 1 such that it is NP-hard to approximate with approximation ratio ρ or better. Nevertheless, in polynomial time it is possible to find an approximation with a ratio of 5/4. That is, this approximation algorithm finds a ...
According to Jensen & Toft (1995), the problem was first formulated by Nelson in 1950, and first published by Gardner (1960). Hadwiger (1945) had earlier published a related result, showing that any cover of the plane by five congruent closed sets contains a unit distance in one of the sets, and he also mentioned the problem in a later paper (Hadwiger 1961).