Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902885 | Discrete Mathematics | 2018 | 10 Pages |
Abstract
In this work we show that the conservative number of a galaxy (a disjoint union of stars) of size M is M for Mâ¡0, 3(mod4), and M+1 otherwise. Consequently, given positive integers m1, m2, â¦, mn with miâ¥3 for 1â¤iâ¤n, we construct a cyclic (m1,m2,â¦,mn)-cycle system of infinitely many circulant graphs, generalizing a result of Bryant, Gavlas and Ling (2003). In particular, it allows us to construct a cyclic (m1,m2,â¦,mn)-cycle system of the complete graph K2M+1, where M=âi=1nmi. Also, we prove necessary and sufficient conditions for the existence of a cyclic (m1,m2,â¦,mn)-cycle system of K2M+2âF, where F is a 1-factor. Furthermore, we give a sufficient condition for a subset of Zvâ{0} to be sequenceable.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Ilan A. Goldfeder, JoaquÃn Tey,