Abstract
AbstractThe existence of 1‐factorizations of an infinite complete equipartite graph (with parts of size ) admitting a vertex‐regular automorphism group is known only when and is countable (i.e., for countable complete graphs) and, in addition, is a finitely generated abelian group of order . In this paper, we show that a vertex‐regular 1‐factorization of under the group exists if and only if has a subgroup of order whose index in is . Furthermore, we provide a sufficient condition for an infinite Cayley graph to have a regular 1‐factorization. Finally, we construct 1‐factorizations that contain a given subfactorization, both having a vertex‐regular automorphism group.
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