The symmetric difference of two cycles is an Eulerian subgraph
In graph theory, a branch of mathematics, a cycle basis of an undirected graph is a set of simple cycles that forms a basis of the cycle space of the graph. That is, it is a minimal set of cycles that allows every even-degree subgraph to be expressed as a symmetric difference of basis cycles.
A fundamental cycle basis may be formed from any spanning tree or spanning forest of the given graph, by selecting the cycles formed by the combination of a path in the tree and a single edge outside the tree. Alternatively, if the edges of the graph have positive weights, the minimum weight cycle basis may be constructed in polynomial time.
In planar graphs, the set of bounded cycles of an embedding of the graph forms a cycle basis. The minimum weight cycle basis of a planar graph corresponds to the Gomory–Hu tree of the dual graph.
cycle basis. There exists a minimum weight cyclebasis in which no two cycles cross each other: for every two cycles in the basis, either the cycles enclose...
The water cycle (or hydrologic cycle or hydrological cycle), is a biogeochemical cycle that involves the continuous movement of water on, above and below...
The cycle rickshaw is a small-scale local means of transport. It is a type of hatchback tricycle designed to carry passengers on a for-hire basis. It...
Smallest Set of Smallest Rings, a cheminformatics term for the minimal cyclebasis of a molecular graph CCCP (disambiguation) USSR (disambiguation) This...
The urea cycle (also known as the ornithine cycle) is a cycle of biochemical reactions that produces urea (NH2)2CO from ammonia (NH3). Animals that use...
evaluate various vehicle and fuel combinations on a full fuel-cycle/vehicle-cyclebasis. The GREET model is specified in the Inflation Reduction Act of...
products. It is also known as the Shewhart cycle, or the control circle/cycle. Another version of this PDCA cycle is OPDCA. The added "O" stands for observation...
The solar cycle, also known as the solar magnetic activity cycle, sunspot cycle, or Schwabe cycle, is a nearly periodic 11-year change in the Sun's activity...
or forest. It is equal to the number of independent cycles in the graph (the size of a cyclebasis). Unlike the corresponding feedback arc set problem...
The cell cycle, or cell-division cycle, is the series of events that take place in a cell that causes it to divide into two daughter cells. These events...
by a suitable authority, fertility charts can be completed on a cycle-by-cyclebasis to show ovulation. This gives the possibility of using the data to...
E − V + 1 fundamental cycles forms a cyclebasis, i.e., a basis for the cycle space. Dual to the notion of a fundamental cycle is the notion of a fundamental...
(the dimension of its cycle space) and vice versa. A cyclebasis of a graph is a set of simple cycles that form a basis of the cycle space (every even-degree...
The Atkinson-cycle engine is a type of internal combustion engine invented by James Atkinson in 1882. The Atkinson cycle is designed to provide efficiency...
cycle is a menstrual cycle characterised by the absence of ovulation and a luteal phase. It may also vary in duration from a regular menstrual cycle....
The nitrogen cycle is the biogeochemical cycle by which nitrogen is converted into multiple chemical forms as it circulates among atmospheric, terrestrial...
design decisions. A cycle-accurate simulator is a computer program that simulates a microarchitecture on a cycle-by-cyclebasis. In contrast an instruction...
level of a rectangular wave is also given by the duty cycle. The pulse wave is used as a basis for other waveforms that modulate an aspect of the pulse...
The carbon cycle is that part of the biogeochemical cycle by which carbon is exchanged among the biosphere, pedosphere, geosphere, hydrosphere, and atmosphere...
economic cycle) are hypothesized cycle-like phenomena in the modern world economy. The phenomenon is closely connected with the technology life cycle. It is...
works and utilities in a way that achieves value for money on a life-cyclebasis while addressing equity principles for sustainable development, therefore...
The estrous cycle (from Latin oestrus 'frenzy', originally from Ancient Greek οἶστρος (oîstros) 'gadfly') is a set of recurring physiological changes...
Basis of Estimate is a tool used in the field of project management by which members of the project team, usually estimators, project managers, or cost...
inputs. Further, forecasts can be computed (on a timely basis). Lastly, uncertainty in business cycles can be gauged, making them useful for assessing macroeconomic...
in entropy (S), Increase in temperature (T) Thermodynamic power cycles are the basis for the operation of heat engines, which supply most of the world's...
generation (DG), vis-à-vis central plants, must be justified on a life-cyclebasis. Unfortunately, many of the direct, and virtually all of the indirect...
curriculum was introduced on a gradual phased basis from 2014, and the process was completed in 2022. A Junior Cycle Profile of Achievement is issued to students...
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