In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph that visits every edge exactly once (allowing for revisiting vertices). Similarly, an Eulerian circuit or Eulerian cycle is …

Jun 8, 2025 · A graph is said to be Eulerian if it contains an Eulerian Cycle, a cycle that visits every edge exactly once and starts and ends at the same vertex. If a graph contains an …

A directed graph is Eulerian iff every graph vertex has equal indegree and outdegree. A planar bipartite graph is dual to a planar Eulerian graph and vice versa.

An Eulerian path on a graph is a traversal of the graph that passes through each edge exactly once. It is an Eulerian circuit if it starts and ends at the same vertex.

Dec 16, 2025 · Is your graph connected? Explain how you know. Determine the degrees of the vertices in the graph. Is your graph an Eulerian graph? Can the postal delivery person visit …

May 19, 2025 · Dive deep into the theory and history of Eulerian paths, including definitions, existence theorems, and step-by-step construction methods.

Nov 3, 2025 · An Eulerian cycle exists if and only if the degrees of all vertices are even. And an Eulerian path exists if and only if the number of vertices with odd degrees is two (or zero, in …

Given any vertex v of G, an Eulerian circuit has to pass through all edges incident with it. Whenever the circuit passes v, it defines a pair consisting of two of these edges.

An Eulerian path is a trail in a graph that visits every edge exactly once. This concept plays a crucial role in understanding the structure of graphs and their connectivity, linking to various …

A connected graph is called Eulerian if there is a sequence v 0, e 1, v 1,…, e k, v k of alternately vertices and edges (where e is an edge joining v−1 and v), with v 0 = v k and with every edge …