The triangle intersection problem for nested Steiner triple systems
نویسندگان
چکیده
We give a solution for the triangle intersection problem for nested Steiner triple systems, with three possible exceptions.
منابع مشابه
Hamilton Decompositions of Block-Intersection Graphs of Steiner Triple Systems
Block-intersection graphs of Steiner triple systems are considered. We prove that the block-intersection graphs of non-isomorphic Steiner triple systems are themselves non-isomorphic. We also prove that each Steiner triple system of order at most 15 has a Hamilton decomposable block-intersection graph.
متن کاملThe Fine Intersection Problem for Steiner Triple Systems
The intersection of two Steiner triple systems (X,A) and (X,B) is the set A ∩ B. The fine intersection problem for Steiner triple systems is to determine for each v, the set I(v), consisting of all possible pairs (m,n) such that there exist two Steiner triple systems of order v whose intersection I satisfies | ∪A∈I A| = m and |I| = n. We show that for v ≡ 1 or 3 (mod 6), |I(v)| = Θ(v3), where p...
متن کاملBlock-Intersection Graphs of Steiner Triple Systems
A Steiner triple system of order n is a collection of subsets of size three, taken from the n-element set {0, 1, ..., n−1}, such that every pair is contained in exactly one of the subsets. The subsets are called triples, and a block-intersection graph is constructed by having each triple correspond to a vertex. If two triples have a non-empty intersection, an edge is inserted between their vert...
متن کاملDecomposing block-intersection graphs of Steiner triple systems into triangles
The problem of decomposing the block intersection graph of a Steiner triple system into triangles is considered. In the case when the block intersection graph has even degree, this is completely solved, while when the block intersection graph has odd degree, removal of some spanning subgraph of odd degree is necessary before the rest can be decomposed into triangles. In this case, some decompos...
متن کاملAlmost all Steiner triple systems have perfect matchings
We show that for any n divisible by 3, almost all order-n Steiner triple systems have a perfect matching (also known as a parallel class or resolution class). In fact, we prove a general upper bound on the number of perfect matchings in a Steiner triple system and show that almost all Steiner triple systems essentially attain this maximum. We accomplish this via a general theorem comparing a un...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 51 شماره
صفحات -
تاریخ انتشار 2011