Hamiltonian decompositions of complete graphs

Symmetric Hamilton cycle decompositions of the complete graph

“…G p defined in Proposition 2.2 is also a symmetric Hamilton cycle decomposition but it is defined only for odd primes p. In Hilton's paper [2], a method for constructing all Hamilton cycle decompositions of K n is given, but a method for constructing a symmetric Hamilton cycle decomposition is not mentioned.…”

Embedding edge‐colorings into 2‐edge‐connected k‐factorizations of kkn+1

“…This problem was solved by Hilton [8] in 1984 using the powerful new technique of amalgamations of graphs, which we describe below (see Figure 2). This technique has been widely successful in several other settings (see for example [ 1,2,9,10]).…”

Maximal sets of Hamilton cycles inKn,n

“…The method of proof used to obtain this result is the method of amalgamations, which is of interest in its own right. It has also been successfully used in similar circumstances (for example, see [5,6,13]). …”