wiki_research

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commit 4fb8794d0cc093c3e7a6a8b1b1fb6eb5bb4ef7c2
parent ded33c5ef61ce2f173eea874b035480a91652140
Author: Antoine Amarilli <a3nm@a3nm.net>
Date:   Thu, 11 Dec 2025 23:26:46 +0100

commit with codex

Diffstat:
algorithms | 1+
circuit | 2+-
counting_algorithm | 7+++++++
counting_problem | 2++
cycle | 2+-
eulerian_circuit | 9+++++++++
eulerian_cycle | 5-----
induced_matching | 9+++++++++
matching | 1+
trail | 2+-
10 files changed, 32 insertions(+), 8 deletions(-)

diff --git a/algorithms b/algorithms @@ -9,6 +9,7 @@ Type: - [algorithm_randomized] - [greedy_algorithm] - [graph_algorithms] +- [counting_algorithm] - [text_algorithms] By date: diff --git a/circuit b/circuit @@ -59,6 +59,6 @@ Up: [theoretical_computer_science] -See also: [sum_product_network], [formula] +See also: [sum_product_network], [formula], [cycle_circuit] Aliases: circuits diff --git a/counting_algorithm b/counting_algorithm @@ -0,0 +1,7 @@ +# Counting algorithm + +An [algorithm] for a [counting_problem] + +- [BEST_theorem] + +Up: [algorithms], [counting_problem] diff --git a/counting_problem b/counting_problem @@ -20,3 +20,5 @@ Up: [computational_problem], [counting] Aliases: counting problems + +See also: [counting_algorithm] diff --git a/cycle b/cycle @@ -7,7 +7,7 @@ In [undirected_graphs], cycles are typically required to have length at least 3 In [directed_graphs], we have [directed_cycles] Variants: -- [circuit_(graph)] if the same [vertices] (but not [edges]) can be visited multiple times +- [cycle_circuit] if the same [vertices] (but not [edges]) can be visited multiple times - like a [trail] compared to a [simple_path] - [tour] if the same [vertices] and [edges] can be visited multiple times - like a [walk] compared to a [simple_path] diff --git a/eulerian_circuit b/eulerian_circuit @@ -0,0 +1,9 @@ +# Eulerian circuit + +An [Eulerian_path] which is a [cycle_circuit], i.e., starts and ends at the same [vertex] + +The number of Eulerian circuits in [directed_graphs] can be computed in [PTIME] by the [BEST_theorem] + +Up: [eulerian_path] + +Aliases: Eulerian cycle diff --git a/eulerian_cycle b/eulerian_cycle @@ -1,5 +0,0 @@ -# Eulerian cycle - -An [Eulerian_path] which is a [cycle], i.e., starts and ends at the same [vertex] - -Up: [eulerian_path] diff --git a/induced_matching b/induced_matching @@ -0,0 +1,9 @@ +# Induced matching + +A [matching] which is an [induced_subgraph] + +Given a [graph], it is [NP_hard] to find a [maximum_induced_matching] + +Up: [matching], [induced_subgraph] + +See also: [mim_width] diff --git a/matching b/matching @@ -17,6 +17,7 @@ Algorithms [graph_algorithm]: Variants: - [matching_variants] +- [induced_matching] - [exact_matching] Also the [linear_relaxation]: see [fractional_edge_packing] diff --git a/trail b/trail @@ -4,6 +4,6 @@ A [walk] where [vertices] can repeat, but not [edges] Up: [path] -See also: [walk], [simple_path] +See also: [walk], [simple_path], [cycle_circuit] Aliases: trails