(i) | $\text{Cycles}(G)$ is a D2744: Set of cycle subgraphs for $G$ |

**acyclic graph**if and only if \begin{equation} \text{Cycles}(G) = \emptyset \end{equation}

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Subset

▾ Power set

▾ Hyperpower set sequence

▾ Hyperpower set

▾ Hypersubset

▾ Subset algebra

▾ Subset structure

▾ Hypergraph

▾ Graph

▾ Path graph

▾ Finite path graph

▾ Cycle graph

▾ Set of cycle subgraphs

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Subset

▾ Power set

▾ Hyperpower set sequence

▾ Hyperpower set

▾ Hypersubset

▾ Subset algebra

▾ Subset structure

▾ Hypergraph

▾ Graph

▾ Path graph

▾ Finite path graph

▾ Cycle graph

▾ Set of cycle subgraphs

Formulation 0

Let $G$ be a D778: Graph such that

Then $G$ is an **acyclic graph** if and only if
\begin{equation}
\text{Cycles}(G)
= \emptyset
\end{equation}

(i) | $\text{Cycles}(G)$ is a D2744: Set of cycle subgraphs for $G$ |

Child definitions