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Covering a Tree by a Forest,s of ., such that every vertex of . is covered exactly once. The.: cover the edges of . by a minimum number of copies of trees of ., such that every edge of . is covered exactly once. For a solution to always exist, we assume that . contains a one vertex (one edge) tree..Two versions of Problem FVC

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Local Search Heuristics for the Multidimensional Assignment Problem, most studied case of MAP is 3-AP, though the problems with larger values of . have also a number of applications. We consider several known and new MAP local search heuristics for MAP as well as their combinations. Computational experiments with three instance families are provided and discussed. A

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Costume

On Related Edges in Well-Covered Graphs without Cycles of Length 4 and 6,status of the problem is not known if the input is restricted to graphs with no cycles of length 4. We conjecture that the problem is polynomial if the input graph does not contain cycles of length 4 and 6, and prove several theorems supporting our conjecture.

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Path-Bicolorable Graphs,if its vertex set . can be partitioned into two subsets (i.e., colors) .. and .. such that for every induced .. (i.e., path with exactly . − 1 edges and . vertices) in ., the two colors alternate along the .., i.e., no two consecutive vertices of the .. belong to the same color .., . = 1,2. Obviousl