commit 5755d442c9f9b5b416180689fff3fdbdbca92ced
parent a365c5efa3e2725c3de93862d52940560756ad1b
Author: Antoine Amarilli <a3nm@a3nm.net>
Date: Thu, 16 Jul 2026 20:05:40 +0200
Merge remote-tracking branch 'origin/master'
Diffstat:
11 files changed, 69 insertions(+), 3 deletions(-)
diff --git a/cycle_double_cover b/cycle_double_cover
@@ -0,0 +1,11 @@
+# Cycle double cover
+
+https://en.wikipedia.org/wiki/Cycle_double_cover
+
+A set of [cycles] in an [undirected_graph] which includes each [edge] exactly twice
+
+- [cycle_double_cover_conjecture]
+
+Up: [graph_covering], [cycle]
+
+See also: [Veblen's_theorem]
diff --git a/cycle_double_cover_conjecture b/cycle_double_cover_conjecture
@@ -0,0 +1,9 @@
+# Cycle double cover conjecture
+
+https://www.openproblemgarden.org/op/cycle_double_cover_conjecture
+
+Every [bridgeless_graph] has a [cycle_double_cover]
+
+See also: [research_ai_mathematics]
+
+Up: [conjecture]
diff --git a/dynamic_word b/dynamic_word
@@ -7,4 +7,4 @@ A [word] on which we can apply [updates_word]
Up: [word]
-Aliases: dynamic words, dynamic string, dynamic strings, dynamic text, dynamic texts
+Aliases: dynamic words, dynamic string, dynamic strings, dynamic text, dynamic texts, incremental maintenance string, incremental maintenance strings
diff --git a/eulerian_circuit b/eulerian_circuit
@@ -2,6 +2,8 @@
A [Eulerian_trail] which is a [cycle_circuit], i.e., starts and ends at the same [vertex]
+An [undirected_graph] has a Eulerian circuit if and only if it is [graph_connected] and the [degree] of each [vertex] is even (this implies in particular that the graph is [bridgeless])
+
The number of Eulerian circuits in [directed_graphs] can be computed in [PTIME] by the [BEST_theorem]
- [Eulerian_circuit_counting]
@@ -9,3 +11,5 @@ The number of Eulerian circuits in [directed_graphs] can be computed in [PTIME]
Up: [eulerian_path]
Aliases: Eulerian cycle, Eulerian circuits
+
+See also: [Veblen's_theorem]
diff --git a/graph_bridgeless b/graph_bridgeless
@@ -5,3 +5,5 @@ A [graph] without a [bridge]
See also: [biconnected_component]
Up: [graph]
+
+Aliases: bridgeless graph, bridgeless graphs, bridgeless
diff --git a/nptime b/nptime
@@ -14,6 +14,6 @@ subset [up]
Up: [complexity_class]
-See also: [ptime], [np_complete], [np_hard], [np_cap_conp], [conp], [nondeterministic_PTIME_Turing_machine]
+See also: [ptime], [np_complete], [np_hard], [np_cap_conp], [conp], [nondeterministic_PTIME_Turing_machine], [P_vs_NP]
Aliases: NP
diff --git a/p_vs_np b/p_vs_np
@@ -0,0 +1,11 @@
+# P vs NP
+
+https://en.wikipedia.org/wiki/P_versus_NP_problem
+
+[open_problem] about the relationship between [nptime] and [ptime]
+
+It is a [Millennium_prize_problem]
+
+https://link.springer.com/article/10.1007/s11704-025-50231-4
+
+Up: [open_problem]
diff --git a/prime_number b/prime_number
@@ -6,6 +6,6 @@
Up: [arithmetic]
-See also: [prime_implicant], [polynomial_irreducible], [twin_prime_conjecture], [goldbach_conjecture], [primitive_word]
+See also: [prime_implicant], [polynomial_irreducible], [twin_prime_conjecture], [goldbach_conjecture], [primitive_word], [twin_primes]
Aliases: prime numbers
diff --git a/twin_prime_conjecture b/twin_prime_conjecture
@@ -0,0 +1,9 @@
+# Twin prime conjecture
+
+https://en.wikipedia.org/wiki/Twin_prime#Twin_prime_conjecture
+
+[conjecture] that there is infinitely many [twin_primes]
+
+related: https://math.stackexchange.com/questions/5142627/recursive-sequence-a-k1-a-k-gcda-k-nk2-1-generating-twin-prim
+
+Up: [conjecture], [twin_primes]
diff --git a/twin_primes b/twin_primes
@@ -0,0 +1,9 @@
+# Twin primes
+
+Two numbers n, n+2 are twin primes if they are both [prime_numbers]
+
+- [twin_prime_conjecture]
+
+Up: [prime_number]
+
+See also: [prime_bounded_gaps]
diff --git a/veblens_theorem b/veblens_theorem
@@ -0,0 +1,11 @@
+# Veblen's theorem
+
+https://en.wikipedia.org/wiki/Veblen%27s_theorem
+
+An [undirected_graph] admits a partition of its edges into [cycles] if and only if every [vertex] has even [degree] (this implies in particular that the graph is [bridgeless])
+
+For [directed_graphs], cf https://math.stackexchange.com/questions/348852/veblens-theorem-for-digraphs
+
+See also: [eulerian_circuit], [cycle_double_cover]
+
+Up: [theorem], [graph_theory]
