[[수학,math]], [[그래프이론,graph_theory]]에서는 순환으로 번역하면 ok?
[[순환,cycle]]
{

(we) (그래프이론에서)
"a '''cycle''' in a [[그래프,graph]] is a non-empty [[trail]] =,trail {  WtEn:trail =    [[트레일,trail]] 자취 흔적 ... }
in which only the first and last vertices''([[버텍스,vertex]])'' are equal.
(중략)
A graph without '''cycles''' is called an [[acyclic_graph]].  // WtEn:acyclic_graph WpEn:acyclic_graph
A [[directed_graph]] without [[directed_cycle]]s is called a [[directed_acyclic_graph]].''([[DAG]])''  // WtEn:directed_graph WpEn:directed_graph
A [[connected_graph]] without '''cycles''' is called a [[트리,tree]]."  // WtEn:connected_graph WpEn:connected_graph

Sub:

[[directed_cycle]] =,directed_cycle =,directed_cycle . directed_cycle
{
directed cycle

WtEn:directed_cycle

semi-twin:
[[WpEn:Cycle_(graph_theory)]]  (Redirected from WpEn:Directed_cycle)
 두번째문장: "A '''directed cycle''' in a [[directed_graph]] is a non-empty [[directed_trail]] in which only the first and last vertices are equal."

Naver:"directed cycle"
Bing:"directed cycle"
Ggl:"directed cycle"
"directed cycle"
}

[[chordless_cycle]] =,chordless_cycle =,chordless_cycle . chordless_cycle
{
chordless cycle

WtEn:chordless_cycle

''WpEn:Chordless_cycle redir to WpEn:Induced_path''
 저기서 함께 묶어 설명하는것들(너무 많은데?) 앞부분:
  "수학의 그래프이론에서,
  '''[[induced_path]] =,induced_path =,induced_path . induced_path { induced path  WtEn:induced_path Ggl:"induced path" }''' in an [[undirected_graph]] $G$ is a [[경로,path]] that is an [[induced_subgraph]] of $G$.
  That is, it is a [[시퀀스,sequence]] of vertices([[버텍스,vertex]]) in $G$ such that
   each two adjacent vertices in the sequence are connected by an [[에지,edge]] in $G$, and
   each two nonadjacent vertices in the sequence are not connected by any edge in $G$.
  An '''induced path''' is sometimes called a snake, and the problem of finding long induced paths in
  '''[[hypercube_graph]] =,hypercube_graph . hypercube_graph { hypercube graph WtEn:hypercube_graph  WpEn:Hypercube_graph Ggl:"hypercube graph" Bing:"hypercube graph" "hypercube graph"}'''
  s is known as the snake-in-the-box problem. // Ggl:"snake-in-the-box problem"
  Similarly, an [[induced_cycle]] is a cycle that is an [[induced_subgraph]] of $G$;
  '''induced cycle'''s are also called [[chordless_cycle]]s or (when the length of the cycle is four or more) [[hole]]s. An [[antihole]] is a hole in the [[complement]]([[컴플리먼트,complement]]) of $G,$ i.e., an antihole is a complement of a hole.
  // Ggl:"graph+theory+hole"
  // Ggl:"graph+theory+antihole"
  The [[길이,length]] of the longest [[induced_path]] in a graph has sometimes been called the [[detour_number]] { detour number  Ggl:"graph detour number" } of the graph;
  for [[sparse_graph]] { sparse graph Ggl:"sparse graph" }s, having bounded detour_number is equivalent to having bounded tree-depth.
  The '''[[induced_path_number]] =,induced_path_number . induced_path_number { induced path number Ggl:"induced path number of graph" }'''
  of a graph $G$ is the smallest number of [[induced_path]]s into which the vertices of the graph may be partitioned, and the closely related
  '''[[path_cover_number]] =,path_cover_number . path_cover_number { path cover number WtEn:path_cover_number  Ggl:"path cover number" "path cover number"}''' of $G$
  is the smallest number of induced_path s that together include all vertices of $G.$
  '''The [[girth]](graph_girth ?) =,girth . girth { Sub:[[odd_girth]]. ...... NdEn:girth KmsE:girth  WtEn:girth Ggl:"graph girth" Ggl:"그래프 girth" }'''
  of a graph is the length of its shortest cycle, but this cycle must be an induced_cycle as any chord could be used to produce a shorter cycle; for similar reasons the [[odd_girth]] of a graph is also the length of its shortest odd induced cycle.

Naver:"chordless cycle"
Bing:"chordless cycle"
Ggl:"chordless cycle"
"chordless cycle"
}

[[induced_cycle]] =,induced_cycle =,induced_cycle . induced_cycle
{
WtEn:induced_cycle

위 chordless cycle 임시참조. 동의어???
}


}

Cmp:
// see [[WpEn:Cycle_(graph_theory)#Circuit_and_cycle]]
[[circuit]]
[[simple_circuit]]
[[directed_circuit]] - cmp [[directed_cycle]]

= 영단어 cycle =
KmsE:cycle - 순환
KpsE:cycle
NdEn:cycle


= Twins =
[[WpEn:Cycle_(graph_theory)]]
= https://en.wikipedia.org/wiki/Cycle_(graph_theory)
= https://en.wikipedia.org/wiki/Cycle_%28graph_theory%29

= (DEL) wikiadmin =
cycle: 사이클 via https://kornorms.korean.go.kr/