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Learn about the problem of finding a path between two vertices in a graph with minimum weight or length. Compare different algorithms and their time complexities for various types of graphs and weights.
Learn about the graph theory problem of finding a shortest closed path that visits every edge of a graph at least once. See the history, applications, variants and algorithms of the Chinese postman problem.
Hall's marriage theorem is a mathematical result that gives a necessary and sufficient condition for the existence of a transversal or a perfect matching in a finite collection of sets or a bipartite graph. The condition is based on the number of elements or neighbors in each subset of sets or vertices.
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 ...
Graph isomorphism is a structure-preserving bijection between graphs, such that adjacent vertices in one graph correspond to adjacent vertices in the other. The graph isomorphism problem is a major unsolved problem in computer science, related to cheminformatics, chemistry and electronic design automation.
Learn about the shortest path algorithm invented by Edsger W. Dijkstra in 1956 and its applications in graph theory and network routing. See the algorithm's pseudocode, history, complexity, and examples.
Kuratowski's theorem is a characterization of planar graphs in terms of two forbidden subgraphs, and K5 and K3,3. Learn the statement, proof, history, and applications of this theorem in graph theory.
Graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. Learn about different types of graphs, their properties, problems and applications in various fields of mathematics, physics, chemistry and biology.