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Bipartite graphs are extensively used in modern coding theory, especially to decode codewords received from the channel. Factor graphs and Tanner graphs are examples of this. A Tanner graph is a bipartite graph in which the vertices on one side of the bipartition represent digits of a codeword, and the vertices on the other side represent combinations of digits that are expected to sum to zero in a codeword without errors.

Bipartite graphs are extensively used in modern coding theory, especially to decode codewords received from the channel. Factor graphs and Tanner graphs are examples of this. A Tanner graph is a bipartite graph in which the vertices on one side of the bipartition represent digits of a codeword, and the vertices on the other side represent combinations of digits that are expected to sum to zero in a codeword without errors.

二分图在现代编码理论中被广泛使用，尤其是对从通道接收到的密码进行解码。例如'''<font color="#ff8000"> 因子图Factor graphs</font>'''和'''<font color="#ff8000"> 坦纳图Tanner graphs</font>'''。Tanner图是二分图，其中二分的一侧顶点表示一个密码数字，另一侧顶点表示一个数字的组合，这些数字的总和期望为零且不存在误差。因子图与置信网络密切相关，用于LDPC和Turbo码的概率解码。

二分图广泛使用于现代编码理论中，尤其是在对从通道接收到的密码进行解码领域。例如'''<font color="#ff8000"> 因子图Factor graphs</font>'''和'''<font color="#ff8000"> 坦纳图Tanner graphs</font>'''。Tanner图是二分图，其中二分的一侧顶点表示一个密码数字，另一侧顶点表示一个数字的组合，这些数字的总和期望为零且不存在误差。因子图与置信网络密切相关，可用于LDPC和Turbo码的概率解码。

In projective geometry, Levi graphs are a form of bipartite graph used to model the incidences between points and lines in a configuration. Corresponding to the geometric property of points and lines that every two lines meet in at most one point and every two points be connected with a single line, Levi graphs necessarily do not contain any cycles of length four, so their girth must be six or more.

In projective geometry, Levi graphs are a form of bipartite graph used to model the incidences between points and lines in a configuration. Corresponding to the geometric property of points and lines that every two lines meet in at most one point and every two points be connected with a single line, Levi graphs necessarily do not contain any cycles of length four, so their girth must be six or more.

在射影几何中，'''<font color="#ff8000"> Levi图</font>'''是二分图的一种形式，用于对配置点和线之间的入射进行建模。对应于点和线的几何特性，即每两条线最多相交一个点，并且每两个点都由一条线连接，因此Levi图不一定包含任何长度为4的环，进而其周长必须为6或更大。

在射影几何中，'''<font color="#ff8000"> Levi图</font>'''是二分图的一种形式，可用于对配置点和线之间的入射进行建模。结合点和线的几何特性，即每两条线最多相交于一个点，并且每两个点都由一条线连接，因此Levi图不一定包含任何长度为4的环，进而其周长必须为6或更大。

== See also 另请参见 ==

== See also 另请参见 ==