Steiner triple systems and strongly regular 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 کاملThe chromatic index of block intersection graphs of Kirkman triple systems and cyclic Steiner triple systems
The block intersection graph of a combinatorial design with block set B is the graph with B as its vertex set such that two vertices are adjacent if and only if their associated blocks are not disjoint. The chromatic index of a graph G is the least number of colours that enable each edge of G to be assigned a single colour such that adjacent edges never have the same colour. A graph G for which...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory
سال: 1969
ISSN: 0021-9800
DOI: 10.1016/s0021-9800(69)80102-x