如何在乳胶中画一条线？

Question

\documentclass[a4paper, 12pt]{article}
\usepackage{amsfonts}
%\usepackage{amsbsy}
\usepackage{amssymb}
\usepackage{amsmath}

\begin{document}

Let $G$ be a $3$-coloured digraph. A subgraph $\mathrm{H}$ of $G$ is called linear if each component of $\mathrm{H}$ is either an edge or a cycle. We call a component of a linear subgraph {\em nonsingular}, if it is a cycle having weight other than $1$. All other components, that is, a cycle of weight $1$ and an edge of any weight, are singular (Laplacian singular, see \cite{DS2}). We use $C_{\mathrm{H}}$ to denote the number of cycles in a linear subgraph $\mathrm{H}$. By $S_{\mathrm{H}}$ and $N_{\mathrm{H}}$, we denote the number of singular components and the number of nonsingular components in $\mathrm{H}$, respectively. By $\mathcal{C}_k$, we will denote the set $\{\mathrm{H}\mid\mathrm{H} \mbox{ is a linear subgraph of order } k \mbox{ of } G \mbox{ in which no cycle has weight } \pm\mathrm{i}\}$.

\end{document}

此处文本中，当我编译时，最后一行超出了框。如何调整此行以使文本不超出范围？

Answer 1

\mbox并且\text不会文本换行，$..$仅对数学部分使用 s。

\documentclass[a4paper, 12pt]{article}
\usepackage{amsfonts}
%\usepackage{amsbsy}
\usepackage{amssymb}
\usepackage{amsmath}

\begin{document}

Let $G$ be a $3$-coloured digraph. A subgraph $\mathrm{H}$ of $G$ is called linear if 
each component of $\mathrm{H}$ is either an edge or a cycle. We call a component of a 
linear subgraph {\em nonsingular}, if it is a cycle having weight other than $1$. All
other components, that is, a cycle of weight $1$ and an edge of any weight, are singular 
(Laplacian singular, see \cite{DS2}). We use $C_{\mathrm{H}}$ to denote the number of 
cycles in a linear subgraph $\mathrm{H}$. By $S_{\mathrm{H}}$ and $N_{\mathrm{H}}$, we 
denote the number of singular components and the number of nonsingular components in 
$\mathrm{H}$, respectively. By $\mathcal{C}_k$, we will denote the set 
\{$\mathrm{H}\mid\mathrm{H}$ is a linear subgraph of order $k$ of $G$ in which no 
cycle has weight $\pm\mathrm{i}$\}.

\end{document}

Answer 2

只是不要使用如此冗长的集合描述：您的读者将很难猜测集合描述的开始和结束位置。

在下面的代码中我添加了几条联系~。

\documentclass[a4paper, 12pt]{article}
\usepackage{amsfonts}
%\usepackage{amsbsy}
\usepackage{amssymb}
\usepackage{amsmath}

\begin{document}

Let $G$ be a $3$-coloured digraph. A subgraph $\mathrm{H}$ of $G$ is called 
linear if each component of $\mathrm{H}$ is either an edge or a cycle. 
We call a component of a linear subgraph \emph{nonsingular}, if it is a cycle 
having weight other than~$1$. All other components, that is, a cycle of 
weight~$1$ and an edge of any weight, are singular (Laplacian singular, 
see~\cite{DS2}). We use $C_{\mathrm{H}}$ to denote the number of cycles in 
a linear subgraph~$\mathrm{H}$. By $S_{\mathrm{H}}$ and $N_{\mathrm{H}}$ 
we denote the number of singular components and the number of nonsingular 
components in~$\mathrm{H}$, respectively. By~$\mathcal{C}_k$ we will denote 
the set 
%%% $\{\mathrm{H}\mid\mathrm{H} \mbox{ is a linear subgraph of order } k 
%%%\mbox{ of } G \mbox{ in which no cycle has weight } \pm\mathrm{i}\}$.
of all linear subgraphs of~$G$ having order~$k$ and in which no cycle has 
weight~$\pm\mathrm{i}$.

\end{document}

还要注意\emph{nonsingular}而不是{\em nonsingular}。我不确定为什么图形符号是斜体，而子图的符号是直立的。

后面需要加逗号吗By~$\mathcal{C}_k$？语法会说不需要。