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)...

have even degree. All Eulerian circuits are also Eulerian paths, but not all Eulerian paths are Eulerian circuits. Euler's work was presented to the St...

\chi (S^{2})=F-E+V=2} Eulerian circuit, Euler cycle or Eulerian path – a path through a graph that takes each edge once Eulerian graph has all its vertices...

open problem on Hamiltonicity of cubic bipartite polyhedral graphs Eulerian path, a path through all edges in a graph Fleischner's theorem, on Hamiltonian...

unicursal in Wiktionary, the free dictionary. Unicursal may refer to: Eulerian path, a sequential set of edges within a graph that reach all nodes Labyrinth...

an Eulerian path if and only if it has either 0 or 2 vertices of odd degree. If it has 0 vertices of odd degree, the Eulerian path is an Eulerian circuit...

which is an NP-hard problem. Eulerian path strategies are computationally more tractable because they try to find a Eulerian path through a deBruijn graph...

Travelling salesman problem – NP-hard problem in combinatorial optimization Eulerian path – Trail in a graph that visits each edge once Capacitated arc routing...

spanning tree. Given an Eulerian graph, we can find an Eulerian tour in ⁠ O ( n ) {\displaystyle O(n)} ⁠ time, so if we had an Eulerian graph with cities from...

such objects. Eulerian An Eulerian path is a walk that uses every edge of a graph exactly once. An Eulerian circuit (also called an Eulerian cycle or an...

unbroken path in an order that surrounds each piece and traverses each edge only once. This process is an application of the Eulerian path. Geometry...

graph Path (graph theory) Seven Bridges of Königsberg Eulerian path Three-cottage problem Shortest path problem Dijkstra's algorithm Open Shortest Path First...

Euclidean traveling salesman problem Euclid's algorithm Euler cycle Eulerian graph Eulerian path exact string matching EXCELL (extendible cell) exchange sort...

infinite family of polyhedral graphs such that the length of the longest simple path of an n {\displaystyle n} -vertex graph in the family is O ( n α ) {\displaystyle...

possible to follow a path that crosses each bridge exactly once. Euler showed that it is not possible: there is no Eulerian path. This solution is considered...

Euclid (as in Euclidean geometry, Euclidean algorithm) Eulerian – Euler (as in Eulerian path) Euripidean – Euripides Eustachian – Eustachius (as in Eustachian...

cycles of the vertices of the five platonic solids – only the octahedron has an Eulerian path or cycle, by extending its path with the dotted one v t e...

constructed by taking a Hamiltonian path of an n-dimensional de Bruijn graph over k symbols (or equivalently, an Eulerian cycle of an (n − 1)-dimensional...

MR 1241401. Pevzner, Pavel A.; Tang, Haixu; Waterman, Michael S. (2001). "An Eulerian path approach to DNA fragment assembly". Proceedings of the National Academy...

integral graph—a graph whose spectrum consists entirely of integers. An Eulerian subgraph of a graph G {\displaystyle G} is a subgraph consisting of a subset...

– euhemerism Leonhard Euler, Swiss mathematician – Euler's formula, Eulerian path, Euler equations; see also: List of topics named after Leonhard Euler...

number of edges, the resulting multigraph does not contain an Eulerian path nor an Eulerian circuit, which means that this puzzle cannot be solved. By bending...

reaching the starting point (in mathematical terminology, this is a Eulerian path on a graph). Children use sticks to draw these in the dirt or sand,...

far. This mirrors the process of the line, which in the theory of the Eulerian path returns to the beginning. Furthermore, Kubik describes sona as being...

shortest closed path or circuit that visits every edge of an (connected) undirected graph at least once. When the graph has an Eulerian circuit (a closed...

In graph theory, a Harris graph is defined as an Eulerian, tough, non-Hamiltonian graph. Harris graphs were introduced in 2013 when, at the University...

macroscopic velocity field. The material derivative can serve as a link between Eulerian and Lagrangian descriptions of continuum deformation. For example, in fluid...

Mathematically, spin ice configurations can be described by closed Eulerian paths. Spin ices are geometrically frustrated magnetic systems. While frustration...

from some Eulerian position x to a corresponding Lagrangian position α forms a problem. Since a fluid parcel with label α traverses along a path of many...

PMC 3290790. PMID 22156294. Pevzner PA; Tang H; Waterman MS (2001). "An Eulerian path approach to DNA fragment assembly". Proceedings of the National Academy...