Sibel Özkan

The Hamilton-Waterloo Problem with 4-Cycles and a Single Factor of n-Cycles

A 2-factor in a graph G is a 2-regular spanning subgraph of G, and a 2-factorization of G is a decomposition of all the edges of G into edge-disjoint 2-factors. A

On one extension of Dirac’s theorem on Hamiltonicity

{\{C_{m}^{r}, C_{n}^{s}\}}

Uniformly Resolvable Cycle Decompositions with Four Different Factors

-factorization of Kυ asks for a 2-factorization of Kυ, where r of the 2-factors consists of m-cycles, and s of the 2-factors consists of n-cycles. This is a case of the Hamilton-Waterloo problem with uniform cycle sizes m and n. If υ is even, then it is a decomposition of Kυ − F where a 1-factor F is removed from Kυ. We present necessary and sufficient conditions for the existence of a

Hall's theorem and extending partial latinized rectangles

{\{C_{4}^{r}, C_{n}^{1}\}}

On the Hamilton-Waterloo Problem with triangle factors and

-factorization of Kυ − F.

C_{3x}

The Hamilton-Waterloo problem with uniform cycle sizes asks for a 2 -factorization of the complete graph K v (for odd v) or K v 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 - 1 2 ? . 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.