In mathematics, an edge cycle cover (sometimes called simply cycle cover[1]) of a graph is a family of cycles which are subgraphs of G and contain all edges of G.
If the cycles of the cover have no vertices in common, the cover is called vertex-disjoint or sometimes simply disjoint cycle cover. In this case, the set of the cycles constitutes a spanning subgraph of G.
If the cycles of the cover have no edges in common, the cover is called edge-disjoint or simply disjoint cycle cover.
^Cun-Quan Zhang, Integer flows and cycle covers of graphs, Marcel Dekker,1997.
mathematics, an edgecyclecover (sometimes called simply cyclecover) of a graph is a family of cycles which are subgraphs of G and contain all edges of G. If...
optimization, cyclecover may refer to: Vertex cyclecover Vertex disjoint cyclecoverEdgecyclecover Other possible meanings include: A cover for a bicycle...
larger graph. If the cycles of the cover have no edges in common, the cover is called edge-disjoint or simply disjoint cyclecover. Similar definitions...
multiset of cycles covering every edge exactly twice? (more unsolved problems in mathematics) In graph-theoretic mathematics, a cycle double cover is a collection...
a metric space. Cycle double cover, a collection of cycles in a graph that together include each edge twice. The cycle double cover conjecture is the...
cover, canonical double cover or simply the bipartite double of G. It should not be confused with a cycle double cover of a graph, a family of cycles...
graph that visits every edge exactly once (allowing for revisiting vertices). Similarly, an Eulerian circuit or Eulerian cycle is an Eulerian trail that...
minimum edgecover is equal to the size of the maximum independent set, and the size of the minimum edgecover plus the size of the minimum vertex cover is...
The Ford Edge is a range of crossover SUVs manufactured by the Ford Motor Company. Introduced for the 2007 model year, the Edge is the first mid-size CUV...
no Hamiltonian cycle C, consider the edges in the cut disconnecting the inner 5-cycle from the outer one. If there is a Hamiltonian cycle, an even number...
for diners, or more abstractly as a problem in graph theory, on the edgecyclecovers of complete graphs. It is named after the Oberwolfach Research Institute...
path is a path whose edges alternate between matched and unmatched edges. An alternating cycle is, similarly, a cycle whose edges alternate between matched...
set or feedback edge set in a directed graph is a subset of the edges of the graph that contains at least one edge out of every cycle in the graph. Removing...
number, cycle rank, or nullity of an undirected graph is the minimum number of edges that must be removed from the graph to break all its cycles, making...
networks. A cycle graph may have its edges colored with two colors if the length of the cycle is even: simply alternate the two colors around the cycle. However...
biclique cover number of a graph G = (V, E) is the minimum number of bicliques (that is complete bipartite subgraphs), needed to cover all edges in E. A...
a Hamiltonian cycle on a directed graph was the enumerative algorithm of Martello. A search procedure by Frank Rubin divides the edges of the graph into...
will create a cycle; such a cycle is called a fundamental cycle with respect to that tree. There is a distinct fundamental cycle for each edge not in the...
edges of a perfect matching) has a vertex cover of size n + k {\displaystyle n+k} . The odd cycle transversal can be transformed into a vertex cover by...
biogeochemical cycles include the carbon cycle, the nitrogen cycle and the water cycle. In each cycle, the chemical element or molecule is transformed and cycled by...
and m edges may be detected in time (n+m2). Atomic cycles are a generalization of chordless cycles, that contain no n-chords. Given some cycle, an n-chord...
between events covered in Arthur. Lawhead later wrote a final book Avalon, which is not considered to be a true addition to the cycle but rather a "related...
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