On the Directed Hamilton-Waterloo Problem with Two Cycle Sizes

Yetgin, Fatih; Odabaşı, UĞUR; Özkan, Sibel

On the Directed Hamilton-Waterloo Problem with Two Cycle Sizes

CONTRIBUTIONS TO DISCRETE MATHEMATICS, cilt.20, sa.1, ss.74-94, 2025 (SCI-Expanded, Scopus)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 20 Sayı: 1
Basım Tarihi: 2025
Dergi Adı: CONTRIBUTIONS TO DISCRETE MATHEMATICS
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
Sayfa Sayıları: ss.74-94
İstanbul Üniversitesi-Cerrahpaşa Adresli: Evet

Özet

The Directed Hamilton-Waterloo Problem asks for a directed 2" role="presentation" >2 $2$ -factorization of the complete symmetric digraph Kv∗" role="presentation" >K∗v $K_{v}^{*}$ where there are two non-isomorphic 2" role="presentation" >2 $2$ -factors. In the uniform version of the problem, factors consist of either directed m" role="presentation" >m $m$ -cycles or n" role="presentation" >n $n$ -cycles. In this paper, necessary conditions for a solution to this problem are given, and the problem is completely solved for the factors with (m,n)∈{(4,6),(4,8),(4,12),(4,16),(6,12),(8,16)}" role="presentation" >(m,n)∈{(4,6),(4,8),(4,12),(4,16),(6,12),(8,16)} $(m, n) \in {(4, 6), (4, 8), (4, 12), (4, 16), (6, 12), (8, 16)}$ . Furthermore, the problem is solved for (m,n)∈{(3,5),(3,15),(5,15)}" role="presentation" >(m,n)∈{(3,5),(3,15),(5,15)} $(m, n) \in {(3, 5), (3, 15), (5, 15)}$ when v" role="presentation" >v $v$ is odd with a few possible exceptions.