topological graph theory, a mathematical discipline, a linkless embedding of an undirected graph is an embedding of the graph into three-dimensional Euclidean...

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...

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...

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...

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...

embedded on any fixed two-dimensional manifold; graphs that are linklessly embeddable in Euclidean 3-space, and graphs that are knotlessly embeddable...

algebraic analogs for the Milnor invariants. A linkless embedding of an undirected graph is an embedding into three-dimensional space such that every two...

matroids and totally unimodular matrices, the four colour theorem, linkless embeddings, graph minors and structure, the perfect graph conjecture, the Hadwiger...

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...

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...

S2CID 209133. Robertson, Neil; Seymour, P. D.; Thomas, Robin (1993), "Linkless embeddings of graphs in 3-space", Bulletin of the American Mathematical Society...

outerplanar; μ ≤ 3 if and only if G is planar; μ ≤ 4 if and only if G is linklessly embeddable in R3. These same families of graphs also show up in connections...

minors and play a role in several other aspects of graph minor theory: linkless embedding, Hadwiger's conjecture, YΔY-reducible graphs, and relations between...

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...

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...

or four are respectively the linear forests, planar graphs, and linklessly embeddable graphs. An outerplanar graph is biconnected if and only if the outer...

theorem for antipodal links and a spectral characterization of linklessly embeddable graphs". Proceedings of the American Mathematical Society. 126 (5):...

theorem Khovanov homology Knot group Knot tabulation Knotless embedding Linkless embedding Link concordance Link group Link (knot theory) Milnor conjecture...

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...

won the 1994 Fulkerson Prize. It follows from their proof that linklessly embeddable graphs, a three-dimensional analogue of planar graphs, have chromatic...

141–148. Robertson, Neil; Seymour, P. D.; Thomas, Robin (1993), "Linkless embeddings of graphs in 3-space", Bulletin of the American Mathematical Society...

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...

the existence of a polynomial-time algorithm for problems such as linkless embedding without allowing the algorithm itself to be explicitly constructed;...

computational complexity as testing whether an embedding of an undirected graph in Euclidean space is linkless. Several algorithms solving the unknotting...

on the M61 Vulcan, mounted internally behind the cockpit, which fires linkless 20 mm ammunition. Wingtip rails can accommodate the AIM-9 Sidewinder missile...

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,...

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...