(we) (그래프이론에서)
"a cycle in a 그래프,graph is a non-empty trail =,trail {
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. //acyclic_graph 
acyclic_graph
A directed_graph without directed_cycles is called a directed_acyclic_graph.(DAG) //directed_graph directed_graph
A connected_graph without cycles is called a 트리,tree." //connected_graph connected_graph
"a cycle in a 그래프,graph is a non-empty trail =,trail {
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. //
acyclic_graph acyclic_graphA directed_graph without directed_cycles is called a directed_acyclic_graph.(DAG) //
directed_graph directed_graphA connected_graph without cycles is called a 트리,tree." //
connected_graph connected_graphSub:
semi-twin:
Cycle_(graph_theory) (Redirected from Directed_cycle)
directed cycle
directed cycle
directed cycle
"directed cycle"
}
Cycle_(graph_theory) (Redirected from 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."
directed cycledirected cycledirected cycle"directed cycle"
}
Chordless_cycle redir to Induced_path저기서 함께 묶어 설명하는것들(너무 많은데?) 앞부분:
"수학의 그래프이론에서,
induced_path =,induced_path =,induced_path . induced_path { induced pathinduced_path induced path } in an undirected_graph $\displaystyle G$ is a 경로,path that is an induced_subgraph of $\displaystyle G$.
That is, it is a 시퀀스,sequence of vertices(버텍스,vertex) in $\displaystyle G$ such that
hypercube_graph =,hypercube_graph . hypercube_graph { hypercube graphhypercube_graph Hypercube_graph hypercube graph hypercube graph "hypercube graph"}
s is known as the snake-in-the-box problem. //snake-in-the-box problem
Similarly, an induced_cycle is a cycle that is an induced_subgraph of $G$;
induced cycles are also called chordless_cycles or (when the length of the cycle is four or more) holes. An antihole is a hole in the complement(컴플리먼트,complement) of $\displaystyle G,$ i.e., an antihole is a complement of a hole.
//graph theory hole
//graph theory antihole
The 길이,length of the longest induced_path in a graph has sometimes been called the detour_number { detour numbergraph detour number } of the graph;
for sparse_graph { sparse graphsparse 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 numberinduced path number of graph }
of a graph $\displaystyle G$ is the smallest number of induced_paths 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 numberpath_cover_number path cover number "path cover number"} of $\displaystyle G$
is the smallest number of induced_path s that together include all vertices of $\displaystyle G.$
The girth(graph_girth ?) =,girth . girth { Sub:[[odd_girth. ......
girth 
girth girth graph girth 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.
induced_path =,induced_path =,induced_path . induced_path { induced path
induced_path induced path } in an undirected_graph $\displaystyle G$ is a 경로,path that is an induced_subgraph of $\displaystyle G$.That is, it is a 시퀀스,sequence of vertices(버텍스,vertex) in $\displaystyle G$ such that
each two adjacent vertices in the sequence are connected by an 에지,edge in $\displaystyle G$, and
each two nonadjacent vertices in the sequence are not connected by any edge in $\displaystyle G$.
An induced path is sometimes called a snake, and the problem of finding long induced paths ineach two nonadjacent vertices in the sequence are not connected by any edge in $\displaystyle G$.
hypercube_graph =,hypercube_graph . hypercube_graph { hypercube graph
hypercube_graph Hypercube_graph hypercube graph hypercube graph "hypercube graph"}s is known as the snake-in-the-box problem. //
snake-in-the-box problemSimilarly, an induced_cycle is a cycle that is an induced_subgraph of $G$;
induced cycles are also called chordless_cycles or (when the length of the cycle is four or more) holes. An antihole is a hole in the complement(컴플리먼트,complement) of $\displaystyle G,$ i.e., an antihole is a complement of a hole.
//
graph theory hole//
graph theory antiholeThe 길이,length of the longest induced_path in a graph has sometimes been called the detour_number { detour number
graph detour number } of the graph;for sparse_graph { sparse graph
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
induced path number of graph }of a graph $\displaystyle G$ is the smallest number of induced_paths 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
path_cover_number path cover number "path cover number"} of $\displaystyle G$is the smallest number of induced_path s that together include all vertices of $\displaystyle G.$
The girth(graph_girth ?) =,girth . girth { Sub:[[odd_girth. ......
girth girth girth graph girth 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.
chordless cyclechordless cyclechordless cycle"chordless cycle"
}
위 chordless cycle 임시참조. 동의어???
}
}
}
Cmp:
// seeCycle_(graph_theory)#Circuit_and_cycle
circuit
simple_circuit
directed_circuit - cmp directed_cycle
// see
Cycle_(graph_theory)#Circuit_and_cyclecircuit
simple_circuit
directed_circuit - cmp directed_cycle
