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The minimum feedback arc set and maximum acyclic subgraph are equivalent for the purposes of exact optimization, as one is the complement set of the other. However, for parameterized complexity and approximation, they differ, because the analysis used for those kinds of algorithms depends on the size of the solution and not just on the size of the input graph, and the minimum feedback arc set ...
Feedback vertex set [2] [3]: GT7 Feedback arc set [2] [3]: GT8 Graph coloring [2] [3]: GT4 Graph homomorphism problem [3]: GT52 Graph partition into subgraphs of specific types (triangles, isomorphic subgraphs, Hamiltonian subgraphs, forests, perfect matchings) are known NP-complete. Partition into cliques is the same problem as coloring the ...
The problem of finding a smallest feedback edge set is equivalent to finding a spanning forest, which can be done in polynomial time. The analogous concept in a directed graph is the feedback arc set (FAS) - a set of directed arcs whose removal makes the graph acyclic. Finding a smallest FAS is an NP-hard problem.
In computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete.In his 1972 paper, "Reducibility Among Combinatorial Problems", [1] Richard Karp used Stephen Cook's 1971 theorem that the boolean satisfiability problem is NP-complete [2] (also called the Cook-Levin theorem) to show that there is a polynomial time many-one reduction ...
Pages in category "Graph theory objects" ... Feedback arc set; Friendly-index set; G. Graceful labeling; Graph center; Graph factorization; H. Hamiltonian decomposition;
Pages in category "Computational problems in graph theory" The following 75 pages are in this category, out of 75 total. ... Feedback arc set; Feedback vertex set ...
The Hamiltonian paths are in one-to-one correspondence with the minimal feedback arc sets of the tournament. [5] Rédei's theorem is the special case for complete graphs of the Gallai–Hasse–Roy–Vitaver theorem , relating the lengths of paths in orientations of graphs to the chromatic number of these graphs.
Feedback arc set, in graph theory, a method of eliminating directed graphs Feedback vertex set , in computational complexity theory, the feedback vertex set problem is a graph-theoretical NP-complete problem