Steiner Triple Systems and Existentially Closed Graphs
نویسندگان
چکیده
منابع مشابه
Steiner Triple Systems and Existentially Closed Graphs
We investigate the conditions under which a Steiner triple system can have a 2or 3-existentially closed block intersection graph.
متن کاملRepresenting graphs in Steiner triple systems - II
Let G = (V,E) be a simple graph and let T = (P,B) be a Steiner triple system. Let φ be a one-to-one function from V to P . Any edge e = {u, v} has its image {φ(u), φ(v)} in a unique block in B. We also denote this induced function from edges to blocks by φ. We say that T represents G if there exists a one-to-one function φ : V → P such that the induced function φ : E → B is also one-to-one; tha...
متن کاملBicolour graphs of Steiner triple systems
In this paper we introduce the notion of a bicolour graph of a Steiner triple system. Given an arbitrary colouring of the points of a Steiner triple system, the bicolour graph is the graph obtained on the point set of the system by placing an edge between two points if they have the same colour and appear in a triple with a point of a di4erent colour. The case where the graph is Kv was partiall...
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 کاملExistentially Closed BIBD Block-Intersection Graphs
A graph G with vertex set V is said to be n-existentially closed if, for every S ⊂ V with |S| = n and every T ⊆ S, there exists a vertex x ∈ V − S such that x is adjacent to each vertex of T but is adjacent to no vertex of S − T . Given a combinatorial design D with block set B, its block-intersection graph GD is the graph having vertex set B such that two vertices b1 and b2 are adjacent if and...
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: The Electronic Journal of Combinatorics
سال: 2005
ISSN: 1077-8926
DOI: 10.37236/1939