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Ramsey graphs and block designs

โœ Scribed by T.D Parsons


Publisher
Elsevier Science
Year
1976
Tongue
English
Weight
483 KB
Volume
20
Category
Article
ISSN
0097-3165

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๐Ÿ“œ SIMILAR VOLUMES


Ramsey unsaturated and saturated graphs
โœ P. Balister; J. Lehel; R.H. Schelp ๐Ÿ“‚ Article ๐Ÿ“… 2005 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 119 KB

## Abstract A graph is __Ramsey unsaturated__ if there exists a proper supergraph of the same order with the same Ramsey number, and __Ramsey saturated__ otherwise. We present some conjectures and results concerning both Ramsey saturated and unsaturated graphs. In particular, we show that cycles __

Zero-sum block designs and graph labelin
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Proving a conjecture of Aigner and Triesch, we show that every graph G = (V,E) without isolated vertices and isolated edges admits an edge labeling 5: E -{0,1}" with binary vectors of length m = [log2 nl + 1 such that the sums 6 ( v ) := 1 ; ; ; &(e) (taken modulo 2 componentwise) are mutually disti

Existential closure of block intersectio
โœ Daniel Horsley; David A. Pike; Asiyeh Sanaei ๐Ÿ“‚ Article ๐Ÿ“… 2011 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 143 KB

A graph G is n-existentially closed (n-e.c.) if for each pair (A,B) of disjoint subsets of V(G) with |A|+|B|โ‰คn there exists a vertex in V(G)\(AโˆชB) which is adjacent to each vertex in A and to no vertex in B. In this paper we study the n-existential closure property of block intersection graphs of in

Existential closure of block intersectio
โœ David A. Pike; Asiyeh Sanaei ๐Ÿ“‚ Article ๐Ÿ“… 2011 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 129 KB

In this article we study the n-existential closure property of the block intersection graphs of infinite t-(v, k, k) designs for which the block size k and the index k are both finite. We show that such block intersection graphs are 2-e.c. when 2 โ‰ค t โ‰ค k-1. When k = 1 and 2 โ‰ค t โ‰ค k, then a necessary