NDLI: Twofold 2-perfect bowtie systems with an extra property

Content Provider	Springer Nature Link
Author	Billington, Elizabeth J. Lindner, C. C. Meszka, Mariusz
Copyright Year	2011
Abstract	A bowtie is a closed trail whose graph consists of two 3-cycles with exactly one vertex in common. A 2-fold bowtie system of order n is an edge-disjoint decomposition of 2K n into bowties. A 2-fold bowtie system is said to be 2-perfect provided that every pair of distinct vertices is joined by two paths of length 2. It is said to be extra provided these two paths always have distinct midpoints. The extra property guarantees that the two paths x, a, y and x, b, y between every pair of vertices form a 4-cycle (x, a, y, b), and that the collection of all such 4-cycles is a four-fold 4-cycle system. We show that the spectrum for extra 2-perfect 2-fold bowtie systems is precisely the set of all n ≡ 0 or 1 (mod 3), $${n\,\geqslant\,6}$$ . Additionally, with an obvious definition, we show that the spectrum for extra 2-perfect 2-fold maximum packings of 2K n with bowties is precisely the set of all n ≡ 2 (mod 3), $${n\,\geqslant\,8}$$ .
Ending Page	153
Page Count	11
Starting Page	143
File Format	PDF
ISSN	00019054
e-ISSN	14208903
Journal	Aequationes mathematicae
Issue Number	1
Volume Number	82
Language	English
Publisher	SP Birkhäuser Verlag Basel
Publisher Date	2011-04-20
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Analysis bowtie Other designs, configurations Combinatorics Complete graph decomposition 2-perfect Paths and cycles
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Discrete Mathematics and Combinatorics

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