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Often, the problem is to decompose a graph into subgraphs isomorphic to a fixed graph; for instance, decomposing a complete graph into Hamiltonian cycles. Other problems specify a family of graphs into which a given graph should be decomposed, for instance, a family of cycles, or decomposing a complete graph K n into n − 1 specified trees ...
Maximum cardinality matching is a fundamental problem in graph theory. [1] We are given a graph G, and the goal is to find a matching containing as many edges as possible; that is, a maximum cardinality subset of the edges such that each vertex is adjacent to at most one edge of the subset. As each edge will cover exactly two vertices, this ...
Outerplanar graph; Random graph; Regular graph; Scale-free network; Snark (graph theory) Sparse graph. Sparse graph code; Split graph; String graph; Strongly regular graph; Threshold graph; Total graph; Tree (graph theory). Trellis (graph) Turán graph; Ultrahomogeneous graph; Vertex-transitive graph; Visibility graph. Museum guard problem ...
Matching (graph theory) MaxDDBS; Maximal independent set; Maximum agreement subtree problem; Maximum common edge subgraph; Maximum common induced subgraph; Maximum cut; Maximum flow problem; Maximum weight matching; Metric k-center; Minimum k-cut; Mixed Chinese postman problem; Multi-trials technique
A few variants of the Chinese Postman Problem have been studied and shown to be NP-complete. [10] The windy postman problem is a variant of the route inspection problem in which the input is an undirected graph, but where each edge may have a different cost for traversing it in one direction than for traversing it in the other direction.
In the mathematical discipline of graph theory, a matching or independent edge set in an undirected graph is a set of edges without common vertices. [1] In other words, a subset of the edges is a matching if each vertex appears in at most one edge of that matching. Finding a matching in a bipartite graph can be treated as a network flow problem.
In graph theory, the blossom algorithm is an algorithm for constructing maximum matchings on graphs. The algorithm was developed by Jack Edmonds in 1961, [1] and published in 1965. [2] Given a general graph G = (V, E), the algorithm finds a matching M such that each vertex in V is incident with at most one edge in M and | M | is maximized. The ...
The "pearls" of the title include theorems, proofs, problems, and examples in graph theory.The book has ten chapters; after an introductory chapter on basic definitions, the remaining chapters material on graph coloring; Hamiltonian cycles and Euler tours; extremal graph theory; subgraph counting problems including connections to permutations, derangements, and Cayley's formula; graph ...