Maximal sets of Hamilton cycles inKn,n

Maximal sets of Hamilton cycles in Dn

“…2(i), A 6 = (0, 1, 6, 3, 5, 4), in which 2 is deleted and in Fig. 2(ii), A 8 = (0, 1,8,2,7,4,6,5), in which 3 is deleted.…”

“…In paper [1], Bryant et al showed that there exists a maximal set S of m edge-disjoint Hamilton cycles in the complete bipartite graph K n,n if and only if n/4 < m n/2. Later, Daven et al [2] showed for n 3 and p 3, there exists a maximal set S of m Hamilton cycles in the complete multipartite graph K p n (p parts of size n) if and only if n(p − 1)/4 m n(p − 1)/2 , and m > n(p − 1)/4 if n is odd and p ≡ 1 (mod 4), except possibly if n is odd and m ((n + 1)(p − 1) − 2)/4.…”

Connectivity and Colorings of Graphs

“…(Or, how many edgedisjoint hamilton cycles could one find in K nyn if a greedy algorithm was used?) The answer turns out to be anywhere from n/4 to n/2 [14]. We have since then tried to solve the corresponding problem when G is a complete multipartite graph, coming very close to a complete answer [39].…”

Maximal sets of hamilton cycles in complete multipartite graphs

“…Very recently, amalgamation techniques have been used by Bryant, El-Zanati, and Rodger [4] to find maximal sets of hamilton cycles in the complete bipartite graph K n;n . They showed the following: Theorem 1.2 [4]. There exists a maximal set of m edge-disjoint hamilton cycles in K n;n , if and only if, n 4 < m n 2 .…”