\usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{lmodern} \usepackage{geometry} \geometry{margin=29mm} \usepackage{amsmath,amssymb,amsthm,mathtools} \usepackage{booktabs} \usepackage{array} \usepackage{enumitem} \usepackage{microtype} \usepackage{xcolor} \usepackage[hidelinks,unicode]{hyperref} \hypersetup{ pdftitle={A Parity Theorem for Reverse-Complement-Invariant Minimum Decycling Sets in q-ary de Bruijn Graphs}, pdfauthor={Oleksiy Babanskyy}, pdfsubject={Research article on reverse-complement-invariant minimum decycling sets}, pdfkeywords={de Bruijn graph, minimum decycling set, reverse complement, complemented alphabet, DNA, unavoidable set} } \setlist{nosep} \setlength{\emergencystretch}{2em} \allowdisplaybreaks \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{remark}[theorem]{Remark} \newcommand{\A}{\mathcal A} \newcommand{\B}{\mathcal B} \newcommand{\RC}{\operatorname{RC}} \newcommand{\PCR}{\operatorname{PCR}} \newcommand{\MDS}{\operatorname{MDS}} \newcommand{\wt}{\operatorname{wt}} \newcommand{\supp}{\operatorname{supp}} \newcommand{\ind}{\mathbf 1} \newcommand{\Nneck}{N_q(k)} \newcommand{\C}{\mathbb C} \newcommand{\Z}{\mathbb Z} \newcommand{\R}{\mathbb R} \newcommand{\eps}{\varepsilon} \newcommand{\tail}{\operatorname{t}} \newcommand{\head}{\operatorname{h}} \newenvironment{boundary}{% \begin{quote}\small\textbf{Claim boundary.}\ }{\end{quote}}