\setlength{\parindent}{0pt}
\setlength{\parskip}{1em}

{
\renewtheorem{customlemma}{Lemma}[part]
\renewtheorem{customtheorem}[customlemma]{Theorem}
\renewtheorem{customproposition}[customlemma]{Proposition}
\renewtheorem{customcorollary}[customlemma]{Corollary}
}
\renewcommand{\thecustomlemma}{\arabic{customlemma}}

\newcommand\abpath[2]{$#1-#2$ path}
\newcommand\abpathpl[2]{$#1$-$#2$ paths}

\newcommand\Ppath{P}

\newcommand\con[1]{\glsref[k_conn]{$#1$-connected}}

\newcommand\edgecon[1]{$#1$-edge-connected}

\newcommand\maxflowmincut{max-flow-min-cut}

\newcommand\vdeg{\glshyperlink[\ensuremath{d}]{v_deg_notation}}

\newcommand\mindeg{\glshyperlink[\ensuremath{\delta}]{min_deg_notation}}
\newcommand\maxdeg{\glshyperlink[\ensuremath{\Delta}]{max_deg_notation}}

\newcommand\nbd{\glshyperlink[\ensuremath{\Gamma}]{nbd_notation}}

\newcommand\complete{\glshyperlink[\ensuremath{K}]{complete_graph_notation}}

\newcommand\bipartite{\glshyperlink[\ensuremath{K}]{complete_bipartite_notation}}

\newcommand\turan{\glshyperlink[\ensuremath{T}]{turan_notation}}

\newcommand\edges{e}

\newcommand\size[1]{|#1|}

\newcommand\gcong{\cong}

\newcommand\rpartite[1]{$#1$-partite}

\newcommand\zaran{\glshyperlink[\ensuremath{Z}]{zaran_notation}}

\newcommand\ex{\glshyperlink[\ensuremath{EX}]{erdos_stone_notation}}

\newcommand\cycle{\glshyperlink[\ensuremath{C}]{cycle_notation}}

\newcommand\bucomplete{\glshyperlink[\ensuremath{K}]{blown_up_complete_notation}}

\newcommand\colset[1]{\glshyperlink[\ensuremath{[#1]}]{colset_notation}}

\newcommand\chromnum{\glshyperlink[\ensuremath{\chi}]{chrom_num_notation}}

\newcommand\vset{V}
\newcommand\eset{E}

\newcommand\rcol[1]{\glsref[r_col]{$#1$-colour}}
\newcommand\rcolring[1]{\glsref[r_col]{$#1$-colouring}}
\newcommand\rcolrings[1]{\glsref[r_col]{$#1$-colourings}}
\newcommand\rcolable[1]{\glsref[r_col]{$#1$-colourable}}
\newcommand\rcoled[1]{\glsref[r_col]{$#1$-coloured}}

\newcommand\kreg[1]{\glsref[regular]{$#1$-regular}}

\newcommand\chrompoly{\glshyperlink[\ensuremath{P}]{chrom_poly_notation}}

\newcommand\emptygraph{\glshyperlink[\ensuremath{E}]{empty_graph_notation}}

\newcommand\edgechromnum{\glshyperlink[\ensuremath{\chi'}]{edge_chrom_num_notation}}

\newcommand\linegraph{\glshyperlink[\ensuremath{L}]{line_graph_notation}}

\newcommand\edgecol[1]{\glshyperlink[$#1$-edge-colouring]{k_edge_col}}

\newcommand\eulerchar{\glshyperlink[\ensuremath{E}]{euler_char_notation}}

\newcommand\heawood{\glshyperlink[\ensuremath{H}]{heawood_notation}}

\newcommand\ramsey{\glshyperlink[\ensuremath{R}]{ramsey_num_notation}}
\newcommand\ramseyd{\glshyperlink[\ensuremath{R}]{ramseyd_num_notation}}
\let\complement\ol

\def\ramseyk_#1(#2){\glshyperlink[\ensuremath{R_{#1}}(#2)]{ramseyk_num_notation}}

\def\xr#1^#2{\glshyperlink[\ensuremath{#1^{(#2)}}]{Xr_notation}}
\def\sq[#1]{\glshyperlink[\ensuremath{[#1]}]{sqb_notation}}

\def\ramseyr^#1{\glshyperlink[\ensuremath{R^{(#1)}}]{ramsey_r_notation}}

\def\psp#1(#2,#3){\glshyperlink[\ensuremath{#1(#2,#3)}]{Gnp_notation}}

\DeclareMathOperator{\internalcliquen}{CL}
\newcommand\cliquen{\glshyperlink[\internalcliquen]{CL_notation}}

\newcommand\indicator[1]{\mathbbm{1}_{#1}}

\newcommand\dist{\glshyperlink[\ensuremath{d}]{dist_notation}}

\newcommand\adjmat{\glshyperlink[\ensuremath{A}]{adj_mat_notation}}

\def\strp(#1,#2,#3){\glshyperlink[\ensuremath{(#1, #2, #3)}]{streg_notation}}
