Zero‐sum block designs and graph labelings

摘要

AbstractProving a conjecture of Aigner and Triesch, we show that every graphG= (V,E) without isolated vertices and isolated edges admits an edge labeling ξ:E→ {0,1}mwith binary vectors of lengthm= log2n + 1 such that the sums.CALLING STATEMENT :(taken modulo 2 componentwise) are mutually distinct, provided thatnis sufficiently large. The proof combines probabilistic arguments with explicitly constructed Steiner systems. © 1995 John WileySons,