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The spectrum for 2-perfect bowtie systems

โœ Scribed by Elizabeth J. Billington; C.C. Lindner

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
409 KB
Volume
135
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

A bowtie is a pair of edge disjoint triangles of K, with a common vertex. A bowtie system is an edge disjoint decomposition of K, into bowties. A bowtie system is 2-perfect if it has the additional property that each bowtie can be replaced by exactly one of its distance 2 graphs so that the resulting collection of bowties is also a bowtie system. We show that the spectrum of 2-perfect bowtie systems is precisely the set of all n = 1 or 9 (mod 12), with the possible exceptions of n=69 and 81. We also solve the same problem for K,\K,.

That is, we show that a 2-perfect decomposition of K,\ K3 into bowties exists if and only if v E 3 or 7 (mod 12).

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