wiki_research

personal research wiki
git clone https://a3nm.net/git/wiki_research/
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commit 49182d31257b760eed4dd522b87c64a09c5e9364
parent 332d7878aef1e9fc40133d97b38ed2f3ea8cc875
Author: Antoine Amarilli <a3nm@a3nm.net>
Date:   Mon, 22 Sep 2025 14:54:00 +0200

Merge branch 'master' of a3nm.net:git/wiki_research

Diffstat:
automata_parikh | 4+++-
circle_packing_theorem | 9+++++++++
hamiltonian_cycle | 12++----------
hamiltonian_cycle_problem | 17+++++++++++++++++
hamiltonian_path | 2+-
hamiltonian_path_problem | 10++++++++++
packing_problem | 1+
string_graph | 11+++++++++++
8 files changed, 54 insertions(+), 12 deletions(-)

diff --git a/automata_parikh b/automata_parikh @@ -4,8 +4,10 @@ https://fr.wikipedia.org/wiki/Automate_de_Parikh introduced in [klaedtke2003monadic] +Also called Z-VASS in [czerwinski2020approach], or integer VASS in [clemente2016separability] + Up: [automata_types] See also: [parikh_image] -Aliases: Parikh automata +Aliases: Parikh automata, Parikh automaton diff --git a/circle_packing_theorem b/circle_packing_theorem @@ -0,0 +1,9 @@ +# Circle packing theorem + +https://en.m.wikipedia.org/wiki/Circle_packing_theorem + +Every [undirected_graph] which is [connected_graph] and [planar_graph] can be achieved as an intersection graph of a [circle_packing] + +Up: [theorem], [packing_problem] + +See also: [intersection_graph], [string_graph] diff --git a/hamiltonian_cycle b/hamiltonian_cycle @@ -1,15 +1,7 @@ # Hamiltonian cycle -[np_hard] +[Computational_problem]: [Hamiltonian_cycle_problem] -[approximation] algorithm: [christofides_heuristic] - -- [hamiltonian_cycle_cube] on [graph_cube] -- [hamiltonian_cycle_square] on [graph_square] -- [hamiltonian_cycle_multiple] going multiple times over each [vertex] - -Special case: [Knight's_tour] - -Up: [problem] on [graph] +Up: [cycle] See also: [graph_eulerian], [hamiltonian_path] diff --git a/hamiltonian_cycle_problem b/hamiltonian_cycle_problem @@ -0,0 +1,17 @@ +# Hamiltonian cycle problem + +The [decision_problem] of whether an input [undirected_graph] admits a [Hamiltonian_cycle], or the [function_problem] of finding one + +It is [NP_hard], like the [Hamiltonian_path_problem] + +[Approximation] algorithm: [christofides_heuristic] + +- [hamiltonian_cycle_cube] on [graph_cube] +- [hamiltonian_cycle_square] on [graph_square] +- [hamiltonian_cycle_multiple] going multiple times over each [vertex] + +Special case: [Knight's_tour] + +Up: [computational_problem], [hamiltonian_cycle] + +See also: [Hamiltonian_path_problem] diff --git a/hamiltonian_path b/hamiltonian_path @@ -2,7 +2,7 @@ A [simple_path] that goes via all vertices of a [graph] -The [computational_problem] of [deciding] whether such a path exists in an input [undirected_graph] is [np_complete] +[Computational_problem]: [Hamiltonian_path_problem] See also: [hamiltonian_cycle], [traveling_salesperson_problem], [k_path], [path_length], [eulerian_path] diff --git a/hamiltonian_path_problem b/hamiltonian_path_problem @@ -0,0 +1,10 @@ +# Hamiltonian path problem + +The [computational_problem] of [deciding] whether an input [undirected_graph] has a [hamiltonian_path] + +It is [np_complete], but it is [FPT] [parameterized] by [treewidth]: +- https://cs.stackexchange.com/questions/59325/an-fpt-algorithm-for-hamiltonian-cycle-running-parameterized-by-treewidth + +Up: [decision_problem], [hamiltonian_path] + +See also: [Hamiltonian_cycle_problem] diff --git a/packing_problem b/packing_problem @@ -9,6 +9,7 @@ - similar looking problem "Heilbronn triangle problem" https://en.wikipedia.org/wiki/Heilbronn_triangle_problem https://www.quantamagazine.org/the-biggest-smallest-triangle-just-got-smaller-20230908/ - conjecture that you can pack any set of [tree] into [clique]: Gyárfás tree packing conjecture - [ringels_conjecture] +- [circle_packing_theorem] Up: [computational_geometry] diff --git a/string_graph b/string_graph @@ -0,0 +1,11 @@ +# String graph + +https://en.m.wikipedia.org/wiki/String_graph + +An [intersection_graph] of curves in the plane + +The [decision_problem] of whether an input [undirected_graph] is of this form is [NP_complete] and the [NP] upper bound is nontrivial + +Up: [graph_family] + +See also: [circle_packing_theorem]