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Sum Coloring
In graph theory, a sum coloring of a graph is a labeling of its vertices by positive integers, with no two adjacent vertices having equal labels, that minimizes the sum of the labels. The minimum sum that can be achieved is called the chromatic sum of the graph. Chromatic sums and sum coloring were introduced by Supowit in 1987 using non-graph-theoretic terminology, and first studied in graph theoretic terms by Ewa Kubicka (independently of Supowit) in her 1989 doctoral thesis. Obtaining the chromatic sum may require using more distinct labels than the chromatic number of the graph, and even when the chromatic number of a graph is bounded, the number of distinct labels needed to obtain the optimal chromatic sum may be arbitrarily large. Computing the chromatic sum is NP-hard. However it may be computed in linear time for tree (graph theory), trees and pseudoforest, pseudotrees, and in polynomial time for outerplanar graphs. There is a constant-factor approximation algorithm for int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tree Sum Coloring
In botany, a tree is a perennial plant with an elongated Plant stem, stem, or trunk (botany), trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, including only woody plants with secondary growth, plants that are usable as lumber or plants above a specified height. In wider definitions, the taller Arecaceae, palms, Cyatheales, tree ferns, Musa (genus), bananas, and bamboos are also trees. Trees are not a Taxon, taxonomic group but include a variety of plant species that Convergent evolution, have independently evolved a trunk and branches as a way to tower above other plants to compete for sunlight. The majority of tree species are angiosperms or hardwoods; of the rest, many are gymnosperms or softwoods. Trees tend to be long-lived, some reaching several thousand years old. Trees have been in existence for 370 million years. It is estimated that there are some three trillion mature trees in the world. A tree typically has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
