Search results
Results from the WOW.Com Content Network
If s and t are specified vertices of the graph G, then an s – t cut is a cut in which s belongs to the set S and t belongs to the set T. In an unweighted undirected graph, the size or weight of a cut is the number of edges crossing the cut. In a weighted graph, the value or weight is defined by the sum of the weights of the edges crossing the ...
Degree diameter problem; Entanglement (graph measure) Erdős–Gyárfás conjecture; Eternal dominating set; Extremal graph theory. Critical graph; Turán's theorem; Frequency partition; Frucht's theorem; Girth; Graph drawing; Graph homomorphism; Graph labeling. Graceful labeling; Graph partition; Graph pebbling; Graph property; Graph reduction ...
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 ...
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
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]
A simple graph contains no double edges or loops. [1] The degree sequence is a list of numbers in nonincreasing order indicating the number of edges incident to each vertex in the graph. [2] If a simple graph exists for exactly the given degree sequence, the list of integers is called graphic. The Havel-Hakimi algorithm constructs a special ...
Zaker (2006) defines a sequence of graphs called t-atoms, with the property that a graph has Grundy number at least t if and only if it contains a t-atom.Each t-atom is formed from an independent set and a (t − 1)-atom, by adding one edge from each vertex of the (t − 1)-atom to a vertex of the independent set, in such a way that each member of the independent set has at least one edge ...
The breadth-first-search algorithm is a way to explore the vertices of a graph layer by layer. It is a basic algorithm in graph theory which can be used as a part of other graph algorithms. For instance, BFS is used by Dinic's algorithm to find maximum flow in a graph.