[algorithm] Difference between hamiltonian path and euler path

Graph Theory Definitions

(In descending order of generality)

  • Walk: a sequence of edges where the end of one edge marks the beginning of the next edge

  • Trail: a walk which does not repeat any edges. All trails are walks.

  • Path: a walk where each vertex is traversed at most once. (paths used to refer to open walks, the definition has changed now) The property of traversing vertices at most once means that edges are also crossed at most once, hence all paths are trails.

Hamiltonian paths & Eulerian trails

  • Hamiltonian path: visits every vertex in the graph (exactly once, because it is a path)

  • Eulerian trail: visits every edge in the graph exactly once (because it is a trail, vertices may well be crossed more than once.)

Examples related to algorithm

How can I tell if an algorithm is efficient? Find the smallest positive integer that does not occur in a given sequence Efficiently getting all divisors of a given number Peak signal detection in realtime timeseries data What is the optimal algorithm for the game 2048? How can I sort a std::map first by value, then by key? Finding square root without using sqrt function? Fastest way to flatten / un-flatten nested JSON objects Mergesort with Python Find common substring between two strings

Examples related to graph

How to plot multiple functions on the same figure, in Matplotlib? Python equivalent to 'hold on' in Matlab How to combine 2 plots (ggplot) into one plot? how to draw directed graphs using networkx in python? What is the difference between dynamic programming and greedy approach? Plotting using a CSV file Python equivalent of D3.js Count number of times a date occurs and make a graph out of it How do I create a chart with multiple series using different X values for each series? Rotating x axis labels in R for barplot

Examples related to graph-theory

Why is the time complexity of both DFS and BFS O( V + E ) Find all paths between two graph nodes When is it practical to use Depth-First Search (DFS) vs Breadth-First Search (BFS)? Difference between hamiltonian path and euler path How to draw a graph in LaTeX? When should I use Kruskal as opposed to Prim (and vice versa)? Find the paths between two given nodes? Finding all cycles in a directed graph Cycles in an Undirected Graph Best algorithm for detecting cycles in a directed graph

Examples related to hamiltonian-path

Difference between hamiltonian path and euler path

Examples related to euler-path

Difference between hamiltonian path and euler path