Tight embeddings of partial quadrilateral packings
نویسندگان
چکیده
منابع مشابه
Tight embeddings of partial quadrilateral packings
Let f(n; C4) be the smallest integer such that, given any set of edge disjoint quadrilaterals on n vertices, one can extend it into a complete quadrilateral decomposition by including at most f(n; C4) additional vertices. It is known, and it is easy to show, that √ n−1 ≤ f(n;C4). Here we settle the longstanding problem that f(n;C4) = √ n+o( √ n). 1 H-packings and H-designs Let H be a simple gra...
متن کاملTight planar packings of two trees
When we consider an embedding of graphs into a plane, it would be nice if it does not intersect internally since the embedding simply shows us the structure of graphs. It is easy to embed a tree into a plane with non-self-intersections. If we embed two or more trees into a plane with non-self-intersections, what occurs? In this paper, we consider embeddings of two trees into a plane with using ...
متن کاملEmbeddings of Simple Maximum Packings of triples with 2 Even
Let MPT (v, 2) denote a maximum packing of triples of order v and index 2. An MPT (v, 2) is called simple if it contains no repeated triples. It is proved in this paper that for v > 2 and any even 2, the necessary and sufficient condition for the embedding of a simple MPT(v,2) in a simple MPT(u,).) is u >/2v + 1.
متن کاملPartial Knowledge in Embeddings
Representing domain knowledge is crucial for any task. There has been a wide range of techniques developed to represent this knowledge, from older logic based approaches to the more recent deep learning based techniques (i.e. embeddings). In this paper, we discuss some of these methods, focusing on the representational expressiveness tradeoffs that are often made. In particular, we focus on the...
متن کاملTight Bounds for $\ell_p$ Oblivious Subspace Embeddings
An lp oblivious subspace embedding is a distribution over r × n matrices Π such that for any fixed n× d matrix A, Pr Π [for all x, ‖Ax‖p ≤ ‖ΠAx‖p ≤ κ‖Ax‖p] ≥ 9/10, where r is the dimension of the embedding, κ is the distortion of the embedding, and for an n-dimensional vector y, ‖y‖p = ( ∑n i=1 |yi|) 1/p is the lp-norm. Another important property is the sparsity of Π, that is, the maximum numbe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2010
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2009.06.003