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--- courses:cs211:winter2014:journals:haley:chapter3 [2014/01/29 04:16] – archermcclellanh
+++ courses:cs211:winter2014:journals:haley:chapter3 [2014/02/12 07:33] (current) – archermcclellanh
@@ Line 44: / Line 44: @@
 ===== 3.4: Testing Bipartiteness =====
-    *
+    * Bipartite graphs contain no odd cycles.
+    * We can use breadth-first search to determine whether a graph is bipartite. We can then say:
+        * No edge of G joins two vertices of the same layer, thus G is bipartite and we can color the even layers one color and the odd another.
+        * xor
+        * An edge joins two vertices in the same layer, G contains an odd-length cycle, so G is not bipartite.
+    * This book section wasn't very interesting. 7/10.
+===== 3.5: Digraphs & Connectivity =====
+    * We represent digraphs as two adjacency lists, one of which is all in-edges and one of which is all out-edges.
+    * BFS & DFS are essentially the same now, with the following changes:
+        * BFS is given by finding all vertices with in-edges from our starting vertex to any other vertex.
+        * DFS is given recursively from vertex //v// by finding a vertex with an edge //v → u//.
+    * A digraph is strongly connected if for every pair of vertices (u,v) there exist paths u → v and v → u.
+        * If two vertices u,v are mutually reachable and v,w are mutually reachable, then u,w are mutually reachable.
+    * The strongly connected components of two vertices in a digraph D are either disjoint or identical.
+    * Well-written and interesting and delightful. 10/10.
+===== 3.6: Directed Acyclic Graphs & Topological Orderings =====
+    * A Directed Acyclic Graph is a directed graph without cycles. Go figure.
+    * They can be used to determine precedence relationships.
+    * A //topological ordering// of a directed graph G is an ordering of its nodes as v_1,v_2,...,v_n such that for each edge (v_i,v_j), i<j.
+    * Iff G is a DAG, it has a topological ordering.
+    * Every DAG necessarily has a vertex with no incoming edges.
+    * We compute topological orderings by finding a vertex in G without incoming edges, putting it first, and deleting it from G. Then recursively find a topo-ordering of G-v and appending that.
+    * This section was okay. 8/10.