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A construction of a perfect set of Euler tours of K 2 k + I
Author(s) -
Verrall H.
Publication year - 1998
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/(sici)1520-6610(1998)6:3<183::aid-jcd2>3.0.co;2-b
Subject(s) - euler's formula , mathematics , corollary , set (abstract data type) , partition (number theory) , euler characteristic , combinatorics , computer science , mathematical analysis , programming language
In this article we define a perfect set of Euler tours of K 2 k + I , I a 1‐factor of K 2 k , to be a set of Euler tours of K 2 k + I that partition the 2‐paths of K 2 k , with the added condition that if ab ∈ I , then each Euler tour contains either the digon a b a or b a b . We prove for all k > 1 that K 2 k + I has a perfect set of Euler tours, and, as a corollary, that L ( K 2 k ) has a Hamilton decomposition. © 1998 John Wiley & Sons, Inc. J Combin Designs 6: 183–211, 1998