Orthogonal H-decompositions

نویسندگان

  • Yair Caro
  • Raphael Yuster
چکیده

An H-decomposition of a graph G is a set L of edge-disjoint Hsubgraphs of G, such that each edge of G appears in some element of L. A k-orthogonal H-decomposition of a graph G is a set of k H-decompositions of G, such that any two copies of H in any two distinct H-decompositions have at most one edge in common. We prove that for every fixed graph H and every fixed integer k ≥ 1, if n is sufficiently large then Kn has a k-orthogonal H decomposition if and only if it has an H-decomposition. This occurs whenever ( n 2 ) is a multiple of e(H) and n− 1 is a multiple of the gcd of the degrees of H.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Orthogonal Decomposition and Packing of Complete Graphs

An H-decomposition of a graph G is a partition of the edge-set of G into subsets, where each subset induces a copy of the graph H. A k-orthogonal H-decomposition of a graph G is a set of k H-decompositions of G, such that any two copies of H in distinct H-decompositions intersect in at most one edge. In case G=Kn and H=Kr , a k-orthogonal Kr -decomposition of Kn is called an (n, r, k) completel...

متن کامل

Orthogonal Decompositions of Complete Digraphs

A family G of isomorphic copies of a given digraph ~ G is said to be an orthogonal decomposition of the complete digraph ~ D n by ~ G, if every arc of ~ D n belongs to exactly two members of G and the union of any two diierent elements from G contains precisely one pair of reverse arcs. Given a digraph ~ H, an ~ H-family m ~ H is the vertex-disjoint union of m copies of ~ H. In this paper, we c...

متن کامل

decompositions , q = 0 limits , and p - adic interpretations of some q - hypergeometric orthogonal polynomials

For little q-Jacobi polynomials, q-Hahn polynomials and big q-Jacobi polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as decompositions into a lower triangular matrix times upper triangular matrix. We develop a general theory of such decompositions rela...

متن کامل

8 N ov 2 00 4 Lower - upper triangular decompositions , q = 0 limits , and p - adic interpretations of some q - hypergeometric orthogonal polynomials Tom

For little q-Jacobi polynomials, q-Hahn polynomials and big q-Jacobi polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as decompositions into a lower triangular matrix times upper triangular matrix. We develop a general theory of such decompositions rela...

متن کامل

Orthogonal Rank Decompositions for Tensors

The theory of orthogonal rank decompositions for matrices is well understood, but the same is not true for tensors. For tensors, even the notions of orthogonality and rank can be interpreted several diierent ways. Tensor decompositions are useful in applications such as principal component analysis for multiway data. We present two types of orthogonal rank decompositions and describe methods to...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2012