sorrachai · yzll0 · May 25, 2026
diff --git a/blueprint/src/Toric.bib b/blueprint/src/Toric.bib
@@ -1,30 +0,0 @@
-@book{Milne_2017,
-    place={Cambridge},
-    series={Cambridge Studies in Advanced Mathematics},
-    title={Algebraic Groups: The Theory of Group Schemes of Finite Type over a Field},
-    publisher={Cambridge University Press},
-    author={Milne, J. S.},
-    year={2017},
-    collection={Cambridge Studies in Advanced Mathematics}
-}
-
-@book{Cox_2011,
-    place={Providence},
-    series={Graduate Studies in Mathematics},
-    title={Toric Varieties},
-    publisher={American Mathematical Society},
-    author={Cox, David A. and Little, John B. and Schenck, H. K.},
-    year={2011},
-    collection={Graduate Studies in Mathematics}
-}
-
-@book{Oda_1988,
-    author = {Oda, Tadao},
-    keywords = {torus embeddings; convex figures in real affine spaces; complex analytic spaces; holomorphic maps; birational geometry; subdivisions of fans; Integral convex polytopes; toric projective varieties; holomorphic differential forms},
-    language = {eng},
-    location = {Berlin [u.a.]},
-    publisher = {Springer},
-    title = {Convex bodies and algebraic geometry},
-    url = {http://eudml.org/doc/203658},
-    year = {1988},
-}

diff --git a/blueprint/src/chapters/1-1-over-cat.tex b/blueprint/src/chapters/1-1-over-cat.tex
diff --git a/blueprint/src/chapters/2-1-tensor-product.tex b/blueprint/src/chapters/2-1-tensor-product.tex
diff --git a/blueprint/src/chapters/Algorithms/Flow/Basic.tex b/blueprint/src/chapters/Algorithms/Flow/Basic.tex
diff --git a/blueprint/src/chapters/Algorithms/MST/Basic.tex b/blueprint/src/chapters/Algorithms/MST/Basic.tex
diff --git a/blueprint/src/chapters/Algorithms/SCC/Basic.tex b/blueprint/src/chapters/Algorithms/SCC/Basic.tex
diff --git a/blueprint/src/chapters/Algorithms/Search/Basic.tex b/blueprint/src/chapters/Algorithms/Search/Basic.tex
diff --git a/blueprint/src/chapters/Algorithms/ShortestPath/Basic.tex b/blueprint/src/chapters/Algorithms/ShortestPath/Basic.tex
diff --git a/blueprint/src/chapters/DataStructures/InverseAckermann.tex b/blueprint/src/chapters/DataStructures/InverseAckermann.tex
@@ -0,0 +1 @@
+\section{Inverse Ackermann}
diff --git a/blueprint/src/chapters/DataStructures/UnionFind/Blueprint.tex b/blueprint/src/chapters/DataStructures/UnionFind/Blueprint.tex
diff --git a/blueprint/src/chapters/Graph/Basic.tex b/blueprint/src/chapters/Graph/Basic.tex
@@ -0,0 +1,18 @@
+\section{Basic}
+
+\begin{definition}
+  An \textit{(undirected) graph} is a pair $G = (V,E)$ consisting of a set $V$ 
+  and a multi-set $E$ of unordered pairs of elements in $V$. 
+  Elements of $V$ are called \textit{vertices} and elements of $E$ are called \textit{edges}.
+  For two vertices $u,v \in V$, we say $u$ and $v$ are \textit{adjacent} if $\{u,v\} \in E$.
+  We call an undirected graph $G$ \textit{simple} if all edges are distinct (i.e., $E$ is a set), 
+  and each edge is a pair of distinct vertices.
+\end{definition}
+
+\begin{definition}
+  A \textit{directed graph} is a pair $G = (V,E)$ consisting of a set $V$ 
+  and a multi-set $E$ of ordered pairs of elements in $V$. 
+  Elements of $V$ are called \textit{vertices} and elements of $E$ are called \textit{edges}.
+  We call a directed graph $G$ \textit{simple} if all edges are distinct and
+  each edge is a pair of distinct vertices.
+\end{definition}
diff --git a/blueprint/src/chapters/Theory/Coloring/Basic.tex b/blueprint/src/chapters/Theory/Coloring/Basic.tex
diff --git a/blueprint/src/chapters/Theory/Connectivity/Basic.tex b/blueprint/src/chapters/Theory/Connectivity/Basic.tex
diff --git a/blueprint/src/chapters/Theory/Embeddings/Basic.tex b/blueprint/src/chapters/Theory/Embeddings/Basic.tex
diff --git a/blueprint/src/chapters/Theory/Matching/Basic.tex b/blueprint/src/chapters/Theory/Matching/Basic.tex
diff --git a/blueprint/src/chapters/Theory/Minors/Basic.tex b/blueprint/src/chapters/Theory/Minors/Basic.tex
diff --git a/blueprint/src/chapters/Theory/Spectral/Basic.tex b/blueprint/src/chapters/Theory/Spectral/Basic.tex
diff --git a/blueprint/src/chapters/Theory/Trees/Basic.tex b/blueprint/src/chapters/Theory/Trees/Basic.tex
diff --git a/blueprint/src/chapters/Theory/Walks/Basic.tex b/blueprint/src/chapters/Theory/Walks/Basic.tex
diff --git a/blueprint/src/content.tex b/blueprint/src/content.tex
@@ -6,13 +6,44 @@
 % the current file can be a simple sequence of \input. Otherwise It
 % can start with a \section or \chapter for instance.
 
+\tableofcontents
 
-\chapter{Introduction}
+\chapter{Graph}
+\input{chapters/Graph/Basic.tex}
 
-\input{chapters/1-1-over-cat.tex} 
+\chapter{Algorithms}
+\section{Flow}
+\input{chapters/Algorithms/Flow/Basic.tex}
+\section{MST}
+\input{chapters/Algorithms/MST/Basic.tex}
+\section{SCC}
+\input{chapters/Algorithms/SCC/Basic.tex}
+\section{Search}
+\input{chapters/Algorithms/Search/Basic.tex}
+\section{Shortest Path}
+\input{chapters/Algorithms/ShortestPath/Basic.tex}
 
-\chapter{Preliminaries}
+\chapter{Data Structures}
+\input{chapters/DataStructures/InverseAckermann.tex}
+\section{Union Find}
+\input{chapters/DataStructures/UnionFind/Blueprint.tex}
+
+\chapter{Theory}
+\section{Coloring}
+\input{chapters/Theory/Coloring/Basic.tex}
+\section{Connectivity}
+\input{chapters/Theory/Connectivity/Basic.tex}
+\section{Embeddings}
+\input{chapters/Theory/Embeddings/Basic.tex}
+\section{Matching}
+\input{chapters/Theory/Matching/Basic.tex}
+\section{Minors}
+\input{chapters/Theory/Minors/Basic.tex}
+\section{Spectral}
+\input{chapters/Theory/Spectral/Basic.tex}
+\section{Trees}
+\input{chapters/Theory/Trees/Basic.tex}
+\section{Walks}
+\input{chapters/Theory/Walks/Basic.tex}
 
-\input{chapters/2-1-tensor-product.tex} 
-
 \input{chapters/biblio}