wiki_research

commit c3eab720625319bfb76be8fc6334eca7a491d8e8
parent 0362651a86607a9d9dc8346f4b9bf559bea08e07
Author: Antoine Amarilli <a3nm@a3nm.net>
Date:   Tue, 25 Aug 2026 20:09:53 +0200

commit with codex

Diffstat:
biconnected_component
 | 
9
+++++++++
block_cut_tree
 | 
7
+++++++
block_graph
 | 
7
+++++++
graph_biconnected
 | 
4
+++-
graph_bipartite
 | 
2
+-
graph_connected
 | 
2
+-

6 files changed, 28 insertions(+), 3 deletions(-)
diff --git a/biconnected_component b/biconnected_component
@@ -0,0 +1,9 @@
+# Biconnected component
+
+A maximal [vertex_induced_subgraph] of a [graph] which is [graph_biconnected]
+
+Up: [graph_biconnected]
+
+See also: [connected_component], [strongly_connected_component], [block_cut_tree], [block_graph]
+
+Aliases: biconnected components
diff --git a/block_cut_tree b/block_cut_tree
@@ -0,0 +1,7 @@
+# Block cut tree
+
+The [bipartite] [tree] obtained from a [connected_graph] by creating one vertex for each [biconnected_component], one vertex for every [articulation_point], and one edge between each [articulation_point] and the [biconnected_components] to which it belongs
+
+See also: [graph_biconnected]
+
+Up: [graph_basic_notions]
diff --git a/block_graph b/block_graph
@@ -0,0 +1,7 @@
+# Block graph
+
+https://en.wikipedia.org/wiki/Block_graph
+
+See also: [biconnected_component], [clique]
+
+Up: [graph_family]
diff --git a/graph_biconnected b/graph_biconnected
@@ -2,8 +2,10 @@
 
 A *biconnected graph* is an [undirected_graph] which is [connected] and has no [cut_vertex]
 
+Equivalently, by [Menger's_theorem], in a biconnected graph featuring at least 3 vertices, between any two distinct vertices you must have two vertex-disjoint paths
+
 Up: [graph_basic_notions]
 
 Aliases: biconnected graph, biconnected graphs, 2-vertex connected graph, 2-vertex connected graphs, 2-vertex connected, 2 vertex connected, 2 vertex connected graph, 2 vertex connected graphs
 
-See also: [biconnected_component], [block_cut_tree]
+See also: [biconnected_component], [block_cut_tree], [block_graph]
diff --git a/graph_bipartite b/graph_bipartite
@@ -9,4 +9,4 @@ Up: [graph_family], [graph_kpartite]
 
 See also: [hypergraph_balanced], [incidence_structure], [3_colorable]
 
-Aliases: bipartite graph, bipartite graphs, 2 colorable
+Aliases: bipartite graph, bipartite graphs, 2 colorable, bipartite
diff --git a/graph_connected b/graph_connected
@@ -6,4 +6,4 @@ See also: [strongly_connected_graph], [graph_biconnected]
 
 Up: [graph]
 
-Aliases: connected graph, connected graphs
+Aliases: connected graph, connected graphs, connected