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Embedding a graph in 3D space with no cycles interlinked
topological graph theory, a mathematical discipline, a linkless embedding of an undirected graph is an embedding of the graph into three-dimensional Euclidean
Linkless_embedding
Embedding a graph in a topological space, often Euclidean
embedding, cellular embedding or map is an embedding in which every face is homeomorphic to an open disk. A closed 2-cell embedding is an embedding in
Graph_embedding
Embedding of the circle in three dimensional Euclidean space
graphs is provided by the graphs with linkless embeddings and knotless embeddings. A linkless embedding is an embedding of the graph with the property that
Knot_(mathematics)
Area of discrete mathematics
embedding (or imbedding) of a graph in surface and linkless embedding, graph minors, crossing number, map coloring, and voltage graph. The embedding of
Graph_theory
Graph in which every two vertices are adjacent
one of the forbidden minors for linkless embedding. In other words, and as Conway and Gordon proved, every embedding of K6 into three-dimensional space
Complete_graph
Graph that can be embedded in the plane
planar graph. A 1-outerplanar embedding of a graph is the same as an outerplanar embedding. For k > 1 a planar embedding is k-outerplanar if removing the
Planar_graph
How many times curves wind around each other
algebraic analogs for the Milnor invariants. A linkless embedding of an undirected graph is an embedding into three-dimensional space such that every two
Linking_number
Cubic graph with 10 vertices and 15 edges
family. These graphs form the forbidden minors for linklessly embeddable graphs, graphs that can be embedded into three-dimensional space in such a way that
Petersen_graph
Finiteness of sets of forbidden graph minors
embedded on any fixed two-dimensional manifold; graphs that are linklessly embeddable in Euclidean 3-space, and graphs that are knotlessly embeddable
Robertson–Seymour_theorem
Planar graphs have straight drawings
straight line embeddings are known to exist for cubic graphs. Sachs (1983) raised the question of whether every graph with a linkless embedding in three-dimensional
Fáry's_theorem
Graph which can be made planar by removing a single node
minors and play a role in several other aspects of graph minor theory: linkless embedding, Hadwiger's conjecture, YΔY-reducible graphs, and relations between
Apex_graph
Graph property
outerplanar; μ ≤ 3 if and only if G is planar; μ ≤ 4 if and only if G is linklessly embeddable in R 3 {\displaystyle \mathbb {R} ^{3}} . These same families of
Colin de Verdière graph invariant
Colin_de_Verdière_graph_invariant
Describing a family of graphs by excluding certain (sub)graphs
S2CID 209133. Robertson, Neil; Seymour, P. D.; Thomas, Robin (1993), "Linkless embeddings of graphs in 3-space", Bulletin of the American Mathematical Society
Forbidden graph characterization
Forbidden_graph_characterization
Holst, Hein (March 2009), "A polynomial-time algorithm to find a linkless embedding of a graph", Journal of Combinatorial Theory, Series B, 99 (2), Elsevier
Glossary_of_graph_theory
Size of largest complete graph made by contracting edges of a given graph
with Hadwiger number at most five include the apex graphs and the linklessly embeddable graphs, both of which have the complete graph K6 among their forbidden
Hadwiger_number
Theorem in geometry about convex sets
theorem for antipodal links and a spectral characterization of linklessly embeddable graphs". Proceedings of the American Mathematical Society. 126 (5):
Radon's_theorem
British mathematician
matroids and totally unimodular matrices, the four colour theorem, linkless embeddings, graph minors and structure, the perfect graph conjecture, the Hadwiger
Paul_Seymour_(mathematician)
Non-crossing graph with vertices on outer face
or four are respectively the linear forests, planar graphs, and linklessly embeddable graphs. An outerplanar graph is biconnected if and only if the outer
Outerplanar_graph
Family of 7 undirected graphs
These seven graphs form the forbidden minors for linklessly embeddable graphs, graphs that can be embedded into three-dimensional space in such a way that
Petersen_family
theorem Khovanov homology Knot group Knot tabulation Knotless embedding Linkless embedding Link concordance Link group Link (knot theory) Milnor conjecture
List_of_knot_theory_topics
Operation on graphs
141–148. Robertson, Neil; Seymour, P. D.; Thomas, Robin (1993), "Linkless embeddings of graphs in 3-space", Bulletin of the American Mathematical Society
YΔ-_and_ΔY-transformation
Unproven generalization of the four-color theorem
won the 1994 Fulkerson Prize. It follows from their proof that linklessly embeddable graphs, a three-dimensional analogue of planar graphs, have chromatic
Hadwiger conjecture (graph theory)
Hadwiger_conjecture_(graph_theory)
Determining whether a knot is the unknot
computational complexity as testing whether an embedding of an undirected graph in Euclidean space is linkless. Several algorithms solving the unknotting
Unknotting_problem
American computer scientist
the existence of a polynomial-time algorithm for problems such as linkless embedding without allowing the algorithm itself to be explicitly constructed;
Michael_Langston
American attack helicopter
2006, a contract was awarded to Meggitt Defense Systems to develop a new linkless 20 mm ammunition handling system to improve on the gun feed reliability
Bell_AH-1Z_Viper
Family of South Korean jet aircraft
on the M61 Vulcan, mounted internally behind the cockpit, which fires linkless 20 mm ammunition. Wingtip rails can accommodate the AIM-9 Sidewinder missile
KAI_T-50_Golden_Eagle
minors. I. e., if a graph G can be embedded linklessly in 3-d space, then every minor of G can also be embedded linklessly. For every two graphs G and H,
Non-constructive algorithm existence proofs
Non-constructive_algorithm_existence_proofs
6 {\displaystyle \mu =6} . In particular, they are neither planar nor linkless. Van der Holst suggested that they might form the complete list of excluded
Heawood_family
LINKLESS EMBEDDING
LINKLESS EMBEDDING
Girl/Female
Hindu
Innocent, Sinless
Boy/Male
Muslim
Innocent, Sinless
Girl/Female
Arabic, Iranian, Muslim, Parsi
Sinless; Innocent
Girl/Female
Indian, Sanskrit
Sinless; Faultless
Boy/Male
Indian, Sanskrit
Sinless; Faultless
Boy/Male
Hindu
Sinless
Girl/Female
Indian, Tamil
Sinless
Boy/Male
Indian
Innocent, Sinless
Girl/Female
Hindu, Indian, Marathi, Tamil
Sinless; Goddess Lakshmi
Boy/Male
Arabic, Muslim
Mindless
Boy/Male
Hindu, Indian, Marathi
Pure; Sinless
Boy/Male
Greek
Lipless.
Boy/Male
Tamil
Mindless
Surname or Lastname
English
English : variant of Winkle.Americanized spelling of German Winkels.
Surname or Lastname
English (West Midlands)
English (West Midlands) : variant spelling of Nicholas.
Girl/Female
Muslim
Innocent, Sinless
Girl/Female
Tamil
Innocent, Sinless
Boy/Male
Indian, Sanskrit
Blameless; Sinless
Boy/Male
Tamil
Sinless
Boy/Male
Indian, Sanskrit
Sinless; Pure
LINKLESS EMBEDDING
LINKLESS EMBEDDING
Male
French
French name derived from Latin Dio, a short form of longer names of Greek origin beginning with Dio-, DION means "Zeus."
Boy/Male
Indian, Sanskrit, Tamil
Lord Venkateswara
Girl/Female
Hindu, Indian, Tamil
Experience; Deer; Goddess Lakshmi
Girl/Female
Bengali, Indian
Honest; Truthful
Male
Egyptian
, a king of Egypt.
Boy/Male
English
From the brook.
Boy/Male
German American Teutonic
Daring.
Surname or Lastname
English
English : nickname from Middle English chow (Old English cēo) ‘jackdaw or crow’.Chinese : variant of Zhou.Chinese : Cantonese variant of Zou.Chinese : variant of Cao 1.Chinese : Cantonese variant of Chao 4.
Girl/Female
Hindu, Indian, Traditional
With Divine Speech
Male
French
Anglo-Norman French form of Middle English Nigel, NIHEL means "champion."
LINKLESS EMBEDDING
LINKLESS EMBEDDING
LINKLESS EMBEDDING
LINKLESS EMBEDDING
LINKLESS EMBEDDING
n.
King-liness.
a.
Negligent; heedless; indolent; listless.
a.
Lifeless; dead.
a.
Destitute of life, or deprived of life; not containing, or inhabited by, living beings or vegetation; dead, or apparently dead; spiritless; powerless; dull; as, a lifeless carcass; lifeless matter; a lifeless desert; a lifeless wine; a lifeless story.
a.
Destitute of a rind.
v. t.
To render inactive or listless.
a.
Having no wings; not able to ascend or fly.
a.
Being without luck; unpropitious; unfortunate; unlucky; meeting with ill success or bad fortune; as, a luckless gamester; a luckless maid.
a.
Having no pulsation; lifeless.
a.
Having no wind; calm.
n.
Want of animation; lifeless; dullness.
a.
Inactive; listless.
a.
Free from sickness.
a.
Wanting wind; out of breath.
n.
Listless indolence; dreaminess. Pope.
a.
destitute of wine; as, wineless life.
a.
Sinless; impeccable.
a.
Lifeless; dead.
a.
Being without lungs.
a.
Hence: Mechanical; indifferent; listless; careless.