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Chordal graphs are precisely the graphs that are both odd-hole-free and even-hole-free (see holes in graph theory). Every chordal graph is a strangulated graph, a graph in which every peripheral cycle is a triangle, because peripheral cycles are a special case of induced
In graph theory, a cycle in a graph is a non-empty trail in which only the first and last vertices are equal. A directed cycle in a directed graph is a non-empty directed trail in which only the first and last vertices are equal. A graph without cycles is called an acyclic graph. A directed graph without directed cycles is called a directed ...
A Hamiltonian cycle, Hamiltonian circuit, vertex tour or graph cycle is a cycle that visits each vertex exactly once. A graph that contains a Hamiltonian cycle is called a Hamiltonian graph . Similar notions may be defined for directed graphs , where each edge (arc) of a path or cycle can only be traced in a single direction (i.e., the vertices ...
Line chart showing the population of the town of Pushkin, Saint Petersburg from 1800 to 2010, measured at various intervals. A line chart or line graph, also known as curve chart, [1] is a type of chart that displays information as a series of data points called 'markers' connected by straight line segments. [2]
Within the cell cycle, there is a stringent set of regulations known as the cell cycle control system that controls the timing and coordination of the phases to ensure a correct order of events. Biochemical triggers known as cyclin-dependent kinases (Cdks) switch on cell cycles events at the corrected time and in the correct order to prevent ...
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.
Suppose that a group element a generates a cycle of order 6 (has order 6), so that the nodes a, a 2, a 3, a 4, a 5, and a 6 = e are the vertices of a hexagon in the cycle graph. The element a 2 then has order 3; but making the nodes a 2 , a 4 , and e be the vertices of a triangle in the graph would add no new information.
It has been proven that every bridgeless graph has cycle k-cover for any even integer k≥4. For k=2, it is the well-known cycle double cover conjecture is an open problem in graph theory. The cycle double cover conjecture states that in every bridgeless graph, there exists a set of cycles that together cover every edge of the graph twice. [3]