From e237c13abe2b87fc23ba06000c342de0e36f8a7c Mon Sep 17 00:00:00 2001
From: Orestis <orestis.malaspinas@pm.me>
Date: Fri, 6 May 2022 10:36:39 +0200
Subject: [PATCH] =?UTF-8?q?ajouts=20d=C3=A9finitions.=20encore=20et=20enco?=
 =?UTF-8?q?re.?=
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---
 slides/cours_24.md                    |  33 ++++++++++++++++++++++++++
 slides/figs/ex_graphe_boucle.pdf      | Bin 0 -> 7497 bytes
 slides/figs/ex_graphe_chaine.pdf      | Bin 0 -> 13306 bytes
 slides/figs/ex_graphe_chaine_elem.pdf | Bin 0 -> 14596 bytes
 4 files changed, 33 insertions(+)
 create mode 100644 slides/figs/ex_graphe_boucle.pdf
 create mode 100644 slides/figs/ex_graphe_chaine.pdf
 create mode 100644 slides/figs/ex_graphe_chaine_elem.pdf

diff --git a/slides/cours_24.md b/slides/cours_24.md
index 1f4a7db..f320971 100644
--- a/slides/cours_24.md
+++ b/slides/cours_24.md
@@ -185,3 +185,36 @@ E&=\{(1,2),(2,3),(2,4),(4,1),(4,2)\},\\
 ![Graphe pondéré orienté (gauche) et non-orienté (droite).](figs/ex_graph_pond.pdf){width=80%}
 
 
+# Généralités
+
+## Définition
+
+* Dans un graphe $G(V,E)$, une **chaîne** reliant un sommet $u$ à un sommet $v$ est une suite d'arêtes entre les sommets, $w_0$, $w_1$, ..., $w_k$, telles que 
+$$
+(w_i, w_{i+1})\in E,\quad u=w_0,\quad v=w_k,\quad \mbox{pour }0\leq i< k,
+$$
+avec $k$ la longueur de la chaîne (le nombre d'arêtes du chemin).
+
+## Exemples
+
+![Illustration d'une chaîne, ou pas chaîne dans un graphe.](figs/ex_graphe_chaine.pdf){width=80%}
+
+# Généralités
+
+## Définition
+
+* Une **chaîne élémentaire** est une chaîne dont tous les sommets sont distincts, sauf les extrémités qui peuvent être égales
+
+## Exemples
+
+![Illustration d'une chaîne élémentaire.](figs/ex_graphe_chaine_elem.pdf){width=80%}
+
+# Généralités
+
+## Définition
+
+* Une **boucle** est une arête $(v,v)$ d'un sommet vers lui-même.
+
+## Exemples
+
+![Illustration d'une boucle.](figs/ex_graphe_boucle.pdf){width=40%}
diff --git a/slides/figs/ex_graphe_boucle.pdf b/slides/figs/ex_graphe_boucle.pdf
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-- 
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