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On Hamilton decompositions of infinite circulant graphs.
- Source :
-
Journal of Graph Theory . Jul2018, Vol. 88 Issue 3, p434-448. 15p. - Publication Year :
- 2018
-
Abstract
- Abstract: The natural infinite analog of a (finite) Hamilton cycle is a two‐way‐infinite Hamilton path (connected spanning 2‐valent subgraph). Although it is known that every connected 2<italic>k</italic>‐valent infinite circulant graph has a two‐way‐infinite Hamilton path, there exist many such graphs that do not have a decomposition into <italic>k</italic> edge‐disjoint two‐way‐infinite Hamilton paths. This contrasts with the finite case where it is conjectured that every 2<italic>k</italic>‐valent connected circulant graph has a decomposition into <italic>k</italic> edge‐disjoint Hamilton cycles. We settle the problem of decomposing 2<italic>k</italic>‐valent infinite circulant graphs into <italic>k</italic> edge‐disjoint two‐way‐infinite Hamilton paths for k = 2, in many cases when k = 3, and in many other cases including where the connection set is ± { 1 , 2 , … , k } or ± { 1 , 2 , … , k − 1 , k + 1 }. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03649024
- Volume :
- 88
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Journal of Graph Theory
- Publication Type :
- Academic Journal
- Accession number :
- 129612187
- Full Text :
- https://doi.org/10.1002/jgt.22223