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A 1-factorization of the line graphs of complete graphs

✍ Scribed by Brian Alspach


Publisher
John Wiley and Sons
Year
1982
Tongue
English
Weight
254 KB
Volume
6
Category
Article
ISSN
0364-9024

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✦ Synopsis


Abstract

A 1‐factorization is constructed for the line graph of the complete graph K~n~ when n is congruent to 0 or 1 modulo 4.


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Extending a result by Hartman and Rosa (1985, Europ. J. Combinatorics 6, 45-48), we prove that for any Abelian group G of even order, except for G Z 2 n with n > 2, there exists a onefactorization of the complete graph admitting G as a sharply-vertex-transitive automorphism group.

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Let n β‰₯ 2 be an integer. The complete graph K n with a 1-factor F removed has a decomposition into Hamilton cycles if and only if n is even. We show that K n -F has a decomposition into Hamilton cycles which are symmetric with respect to the 1-factor F if and only if n ≑ 2,4 mod 8. We also show that