Intrinsically Triple Linked Complete Graphs
نویسندگان
چکیده
We prove that every embedding of K10 in R3 contains a non-split link of three components. We also exhibit an embedding of K9 with no such link of three components.
منابع مشابه
N ov 2 00 8 Intrinsically triple - linked graphs in R P 3 ∗
Flapan, et al [8] showed that every spatial embedding of K 10 , the complete graph on ten vertices, contains a non-split three-component link (K 10 is intrinsically triple-linked). The papers [2] and [7] extended the list of known in-trinsically triple-linked graphs in R 3 to include several other families of graphs. In this paper, we will show that while some of these graphs can be embedded 3-...
متن کاملGraphs that are intrinsically linked with an unused vertex
We examine graphs that, for every spatial embedding, have a pair of linked cycles such that linked cycles do not pass through every vertex of the graph (we call such a graph intrinsically linked with an unused vertex). We demonstrate three graph operations that transform an intrinsically linked graph to a graph with this property. It remains an open question to determine all minor-minimal graph...
متن کاملIntrinsic Linking and Knotting of Graphs
An analog to intrinsic linking, intrinsic even linking, is explored in the first half of this paper. Four graphs are established to be minor minimal intrinsically even linked, and it is conjectured that they form a complete minor minimal set. Some characterizations are given, using the simplest of the four graphs as an integral part of the arguments, that may be useful in proving the conjecture...
متن کاملIntrinsic Linking and Knotting of Graphs in Arbitrary 3–manifolds
We prove that a graph is intrinsically linked in an arbitrary 3-manifold M if and only if it is intrinsically linked in S. Also, assuming the Poincaré Conjecture, a graph is intrinsically knotted in M if and only if it is intrinsically knotted in S.
متن کاملIntrinsically linked signed graphs in projective space
We define a signed embedding of a signed graph into real projective space to be an embedding such that an embedded cycle is 0-homologous if and only if it is balanced. We characterize signed graphs that have a linkless signed embedding. In particular, we exhibit 46 graphs that form the complete minor-minimal set of signed graphs that contain a nonsplit link for every signed embedding. With one ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000