Everything about Linkless embedding
Embedding a graph in 3D space with no cycles interlinked
In topological graph theory, a mathematical discipline, a linkless embedding of an undirected graph is an embedding of the graph into three-dimensional Euclidean space in such a way that no two cycles of the graph are linked. A flat embedding is an embedding with the property that every cycle is the boundary of a topological disk whose interior is disjoint from the graph. A linklessly embeddable graph is a graph that has a linkless or flat embedding; these graphs form a three-dimensional analogue of the planar graphs. Complementarily, an intrinsically linked graph is a graph that does not have a linkless embedding. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Linkless embeddingA 5-minute orientation
- Read the landmark paper: Sachs′ Linkless Embedding ConjectureCited 106 times
- Go sideways: Petersen familyA closely related topic
- Go sideways: Apex graphA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Sachs′ Linkless Embedding Conjecture
Linkless embeddings of graphs in 3-space
A polynomial-time algorithm to find a linkless embedding of a graph
Linkless and Flat Embeddings in 3-Space
Framed 4-valent graph minor theory I: Introduction. A planarity criterion and linkless embeddability
Linear linkless embeddings: proof of a conjecture by Sachs
📚 Books worth reading
Open Library didn't respond; try again in a moment.
🔗 Related topics
- Petersen family In graph theory, the Petersen family is a set of seven undirected graphs that includes the Petersen graph and the complete graph K6. The Petersen family…
- Apex graph In graph theory, a branch of mathematics, an apex graph is a graph that can be made planar by the removal of a single vertex. The deleted vertex is called…
- YΔ- and ΔY-transformation In graph theory, ΔY- and YΔ-transformations (also written delta-wye and wye-delta) are a pair of operations on graphs. A ΔY-transformation replaces a triangle…
- Heawood family In graph theory the term Heawood family refers to either one of the following two related graph families generated via ΔY- and YΔ-transformations: the…
- Graph minor In graph theory, an undirected graph H is called a minor of the undirected graph G if H can be formed from G by deleting edges and vertices and by contracting…
- Complete graph In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique…
- Planar graph In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect…
- Planar cover In graph theory, a planar cover of a finite graph G is a finite covering graph of G that is itself a planar graph. Every graph that can be embedded into…