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When the degree is less than or equal to 2 or the diameter is less than or equal to 1, the problem becomes trivial, solved by the cycle graph and complete graph respectively. In graph theory, the degree diameter problem is the problem of finding the largest possible graph G (in terms of the size of its vertex set V) of diameter k such that the ...
Pages in category "Computational problems in graph theory" The following 75 pages are in this category, out of 75 total. This list may not reflect recent changes .
The works of Ramsey on colorations and more specially the results obtained by Turán in 1941 was at the origin of another branch of graph theory, extremal graph theory. The four color problem remained unsolved for more than a century. In 1969 Heinrich Heesch published a method for solving the problem using computers. [29]
Breadth-first search can be used to solve many problems in graph theory, for example: Copying garbage collection, Cheney's algorithm; Finding the shortest path between two nodes u and v, with path length measured by number of edges (an advantage over depth-first search) [14] (Reverse) Cuthill–McKee mesh numbering
The problems of finding a Hamiltonian path and a Hamiltonian cycle can be related as follows: In one direction, the Hamiltonian path problem for graph G can be related to the Hamiltonian cycle problem in a graph H obtained from G by adding a new universal vertex x, connecting x to all vertices of G. Thus, finding a Hamiltonian path cannot be ...
3-dimensional matchings. (a) Input T. (b)–(c) Solutions. In the mathematical discipline of graph theory, a 3-dimensional matching is a generalization of bipartite matching (also known as 2-dimensional matching) to 3-partite hypergraphs, which consist of hyperedges each of which contains 3 vertices (instead of edges containing 2 vertices in a usual graph).
Shortest path (A, C, E, D, F), blue, between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.
The problem of constructing a solution for the graph realization problem with the additional constraint that each such solution comes with the same probability was shown to have a polynomial-time approximation scheme for the degree sequences of regular graphs by Cooper, Martin, and Greenhill. [5] The general problem is still unsolved.