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Forest, a cycle-free graph; Line perfect graph, a graph in which every odd cycle is a triangle; Perfect graph, a graph with no induced cycles or their complements of odd length greater than three; Pseudoforest, a graph in which each connected component has at most one cycle; Strangulated graph, a graph in which every peripheral cycle is a triangle
A chart created with data from a Microsoft Excel spreadsheet that only saves the chart. To save the chart and spreadsheet save as .XLS. XLC is not supported in Excel 2007 or in any newer versions of Excel. Dialog .xld: Used in older versions of Excel. Archive .xlk: A backup of an Excel Spreadsheet Add-in (DLL) .xll
A directed cycle graph of length 8. A directed cycle graph is a directed version of a cycle graph, with all the edges being oriented in the same direction. In a directed graph, a set of edges which contains at least one edge (or arc) from each directed cycle is called a feedback arc set.
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 ...
A path in a directed graph is a sequence of edges having the property that the ending vertex of each edge in the sequence is the same as the starting vertex of the next edge in the sequence; a path forms a cycle if the starting vertex of its first edge equals the ending vertex of its last edge. A directed acyclic graph is a directed graph that ...
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.
The circuit rank controls the number of ears in an ear decomposition of a graph, a partition of the edges of the graph into paths and cycles that is useful in many graph algorithms. In particular, a graph is 2-vertex-connected if and only if it has an open ear decomposition. This is a sequence of subgraphs, where the first subgraph is a simple ...
A path is a particularly simple example of a tree, and in fact the paths are exactly the trees in which no vertex has degree 3 or more. A disjoint union of paths is called a linear forest . Paths are fundamental concepts of graph theory, described in the introductory sections of most graph theory texts.