Editing Cycle (graph theory) (section)

== Graph classes defined by cycle ==
Several important classes of graphs can be defined by or characterized by their cycles. These include:
* [[Bipartite graph]], a graph without odd cycles (cycles with an odd number of vertices)
* [[Cactus graph]], a graph in which every nontrivial biconnected component is a cycle
* [[Cycle graph]], a graph that consists of a single cycle
* [[Chordal graph]], a graph in which every induced cycle is a triangle
* [[Directed acyclic graph]], a directed graph with no directed cycles
* [[Forest (graph theory)|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
* [[Strongly connected graph]], a directed graph in which every edge is part of a cycle
* [[Triangle-free graph]], a graph without three-vertex cycles
* [[Even-cycle-free graph]], a graph without even cycles
* [[Even-hole-free graph]], a graph without even cycles of length larger or equal to 6