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Zero‐sum delta‐systems and multiple copies of graphs
Author(s) -
Caro Yair,
Provstgaard Christian
Publication year - 1999
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/(sici)1097-0118(199910)32:2<207::aid-jgt9>3.0.co;2-3
Subject(s) - combinatorics , mathematics , discrete mathematics , graph , zero (linguistics) , extremal graph theory , line graph , voltage graph , philosophy , linguistics
A main result proved in this paper is the following. Theorem. Let G be a noncomplete graph on n vertices with degree sequence d 1 ≥ d 2 ≥ · · · ≥ d n and t ≥ 2 be a prime. Let m = gcd { t, d i − d j : 1 ≤ i < j ≤ n } and set$$d =\cases{1\ \ \ if\ m = t\ and\ \ m \not\mid\ d_{i}\ for\ 1 \leq i \leq n \cr 0\ \ \ otherwise.}$$ Then R ( tG , ℤ t ) = t ( n + d ) − d , where R is the zero‐sum Ramsey number. This settles, almost completely, problems raised in [Bialostocki & Dierker, J Graph Theory, 1994; Y. Caro, J Graph Theory, 1991]. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 207–216, 1999