Königsberg city had seven bridges connecting two islands and mainland. Problem required crossing each bridge once through city. Euler proved problem has no solution in 1736
A cycle is a non-empty trail where only first and last vertices are equal. A graph without cycles is called acyclic or directed acyclic. A connected graph without cycles is called a tree
Dijkstra's algorithm was developed in 1956 for finding shortest paths in weighted graphs. Algorithm was published in 1959, two years after Prim's and 29 years after Jarník. Designed to demonstrate ARMAC computer capabilities while working at Amsterdam Mathematical Center
Hamiltonian path visits each vertex exactly once in a graph. Hamiltonian cycle visits each vertex exactly once. Hamiltonian paths can be completed by adding edges to adjacent vertices. Hamiltonian cycles can be converted to paths by removing edges
A tree is an undirected graph where any two vertices are connected by exactly one path. A forest is an undirected graph where any two vertices are connected by at most one path. A rooted tree has one designated vertex called the root
Greedy algorithms find optimal solutions in shortest time possible. Edsger Dijkstra introduced term for minimum spanning tree calculations. Prim and Kruskal developed optimization techniques for graph problems