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Zero-sum block designs and graph labelings

✍ Scribed by Zsolt Tuza

Publisher: John Wiley and Sons
Year: 1995
Tongue: English
Weight: 621 KB
Volume: 3
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.3180030203

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✦ Synopsis

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 distinct, provided that n is sufficiently large. The proof combines probabilistic arguments with explicitly constructed Steiner systems.

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