A complete solution to the infinite Oberwolfach problem. Issue 5 (5th February 2020)

• Record Type: Journal Article
• Authors: Costa, Simone
• Is Part Of: Journal of combinatorial designs. Volume 28:Issue 5(2020:May)
• Page Start: 366
• Page End: 383
• Publication Date: 2020-02-05
• Subjects: regular factorizations -- Oberwolfach problem -- subsystems; Combinatorial designs and configurations -- Periodicals; Configurations et schémas combinatoires -- Périodiques; 511.6
• DOI: 10.1002/jcd.21702
• Languages: English
• ISSNs: 1063-8539

Abstract

Abstract: Let F be a 2‐regular graph of order v . The Oberwolfach problem, OP ( F ), asks for a 2‐factorization of the complete graph on v vertices in which each 2‐factor is isomorphic to F . In this paper, we give a complete solution to the Oberwolfach problem over infinite complete graphs, proving the existence of solutions that are regular under the action of a given involution free group G . We will also consider the same problem in the more general context of graphs F that are spanning subgraphs of an infinite complete graph K and we provide a solution when F is locally finite. Moreover, we characterize the infinite subgraphs L of F such that there exists a solution to OP ( F ) containing a solution to OP ( L ).