From 180e7cd44e925d991f3a7f92bcc512a3934f03ac Mon Sep 17 00:00:00 2001
From: Antti H S Laaksonen <ahslaaks@cs.helsinki.fi>
Date: Sat, 25 Feb 2017 19:39:04 +0200
Subject: [PATCH] References etc.

---
 chapter20.tex |  6 +++---
 list.tex      | 17 +++++++++++++++++
 2 files changed, 20 insertions(+), 3 deletions(-)

diff --git a/chapter20.tex b/chapter20.tex
index 1e7a8d0..9ca3eb0 100644
--- a/chapter20.tex
+++ b/chapter20.tex
@@ -930,7 +930,7 @@ The maximum flow of this graph is as follows:
 \index{Hall's theorem}
 \index{perfect matching}
 
-\key{Hall's theorem} can be used to find out
+\key{Hall's theorem} \cite{hal35} can be used to find out
 whether a bipartite graph has a matching
 that contains all left or right nodes.
 If the number of left and right nodes is the same,
@@ -1020,7 +1020,7 @@ has at least one endpoint in the set.
 In a general graph, finding a minimum node cover
 is a NP-hard problem.
 However, if the graph is bipartite,
-\key{Kőnig's theorem} tells us that
+\key{Kőnig's theorem} \cite{kon31} tells us that
 the size of a minimum node cover
 and the size of a maximum matching are always equal.
 Thus, we can calculate the size of a minimum node cover
@@ -1409,7 +1409,7 @@ An \key{antichain} is a set of nodes of a graph
 such that there is no path
 from any node to another node
 using the edges of the graph.
-\key{Dilworth's theorem} states that
+\key{Dilworth's theorem} \cite{dil50} states that
 in a directed acyclic graph, the size of
 a minimum general path cover
 equals the size of a maximum antichain.
diff --git a/list.tex b/list.tex
index da165ec..0958ad3 100644
--- a/list.tex
+++ b/list.tex
@@ -44,6 +44,11 @@
   A note on two problems in connexion with graphs.
   \emph{Numerische Mathematik}, 1(1):269--271, 1959.
 
+\bibitem{dil50}
+  R. P. Dilworth.
+  A decomposition theorem for partially ordered sets.
+  \emph{Annals of Mathematics}, 51(1):161--166, 1950.
+
 \bibitem{dir52}
   G. A. Dirac.
   Some theorems on abstract graphs.
@@ -117,6 +122,13 @@
   Computer Science and Computational Biology},
   Cambridge University Press, 1997.
 
+\bibitem{hal35}
+  P. Hall.
+  On representatives of subsets.
+  \emph{Journal London Mathematical Society} 10(1):26--30, 1935.
+
+  On representatives of subsets. J. London Math. Soc, 10(1), 26-30.
+
 \bibitem{hel62}
   M. Held and R. M. Karp.
   A dynamic programming approach to sequencing problems.
@@ -164,6 +176,11 @@
   D. E. Knuth.
   \emph{The Art of Computer Programming. Volume 3: Sorting and Searching}, Addison–Wesley, 1998 (2nd edition).
 
+\bibitem{kon31}
+  D. Kőnig.
+  Gráfok és mátrixok.
+  \emph{Matematikai és Fizikai Lapok}, 38(1):116--119, 1931.
+
 \bibitem{kru56}
   J. B. Kruskal.
   On the shortest spanning subtree of a graph and the traveling salesman problem.