"수학의 그래프이론에서,
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 in
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 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 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.