Q5‐factorization of λKn Doğan, Oğuz; Küçükçifçi, Selda; Yazıcı, Emine Ş.
Journal of combinatorial designs,
20/May , Letnik:
28, Številka:
5
Journal Article
Recenzirano
Qk is the simple graph whose vertices are the k‐tuples with entries in {0, 1} and edges are the pairs of k‐tuples that differ in exactly one position. In this paper, we proved that there exists a ...Q5‐factorization of λKn if and only if (a) n ≡ 0(mod 32) if λ ≡ 0(mod 5) and (b) n ≡ 96(mod 160) if λ ≢ 0(mod 5).
The complete multipartite graph
K
n
(
m
)
with
n parts of size
m is shown to have a decomposition into
n-cycles in such a way that each cycle meets each part of
K
n
(
m
)
; that is, each cycle is ...said to be
gregarious. Furthermore, gregarious decompositions are given which are also resolvable.
The Hamilton–Waterloo problem with uniform cycle sizes asks for a 2-factorization of the complete graph Kv (for odd v) or Kv minus a 1-factor (for even v) where r of the factors consist of n-cycles ...and s of the factors consist of m-cycles with r+s=⌊v−12⌋. In this paper, the Hamilton–Waterloo Problem with 4-cycle and m-cycle factors for odd m≥3 is studied and all possible solutions with a few possible exceptions are determined.
In this paper, we consider uniformly resolvable decompositions of complete graph
K
v
(or
K
v
minus a 1-factor
I
for even
v
) into cycles. We will focus on the existence of factorizations of
K
v
or
K
...v
-
I
containing up to four non-isomorphic factors. We obtain all possible solutions for uniform factors involving 4,
m
, 2
m
and 4
m
-cycles with a few possible exceptions when
m
is odd.
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