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A complete solution to the infinite Oberwolfach problem
Author(s) -
Costa Simone
Publication year - 2020
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21702
Subject(s) - mathematics , combinatorics , factorization , graph , discrete mathematics , algorithm
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 ).