Search results
Results from the WOW.Com Content Network
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 ...
This graph becomes disconnected when the right-most node in the gray area on the left is removed This graph becomes disconnected when the dashed edge is removed.. In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more ...
The induced subgraph isomorphism problem is a form of the subgraph isomorphism problem in which the goal is to test whether one graph can be found as an induced subgraph of another. Because it includes the clique problem as a special case, it is NP-complete. [4]
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.
The edge bipartization problem is the algorithmic problem of deleting as few edges as possible to make a graph bipartite and is also an important problem in graph modification algorithmics. This problem is also fixed-parameter tractable , and can be solved in time O ( 2 k m 2 ) {\textstyle O\left(2^{k}m^{2}\right)} , [ 33 ] where k is the ...
This category lists computational problems that arise in graph theory. Subcategories. This category has the following 4 subcategories, out of 4 total. G.
If there are multiple maximum independent sets, only one need be output. This problem is sometimes referred to as "vertex packing". In the maximum-weight independent set problem, the input is an undirected graph with weights on its vertices and the output is an independent set with maximum total weight. The maximum independent set problem is ...
Deciding whether the metric dimension of a tree is at most a given integer can be done in linear time [10] Other linear-time algorithms exist for cographs, [5] chain graphs, [11] and cactus block graphs [12] (a class including both cactus graphs and block graphs). The problem may be solved in polynomial time on outerplanar graphs. [4]