On Hamilton decompositions of infinite circulant graphs

Bryant, Darryn; Herke, Sarada; Maenhaut, Barbara and Webb, Bridget S. (2017). On Hamilton decompositions of infinite circulant graphs. Journal of Graph Theory, 88(3) pp. 434–448.

DOI: https://doi.org/10.1002/jgt.22223

Abstract

The natural infinite analogue of a (finite) Hamilton cycle is a two-way-infinite Hamilton path (connected spanning 2-valent subgraph). Although it is known that every connected 2k-valent infinite circulant graph has a two-way-infinite Hamilton path, there exist many such graphs that do not have a decomposition into k edge-disjoint two-way-infinite Hamilton paths. This contrasts with the finite case where it is conjectured that every 2k-valent connected circulant graph has a decomposition into k edge-disjoint Hamilton cycles. We settle the problem of decomposing 2k-valent infinite circulant graphs into k 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, 1,2,...,k + 1}.

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About

• Item ORO ID
• 52560
• Item Type
• Journal Item
• ISSN
• 0364-9024
• Project Funding Details

• Funded Project Name	Project ID	Funding Body
  Homogeneous Steiner triple systems	Not Set	EPSRC (Engineering and Physical Sciences Research Council)
  Not Set	Not Set	ARC Australian Research Council
  Not Set	Not Set	ARC Australian Research Council
  Not Set	Not Set	ARC Australian Research Council
  Not Set	Not Set	ARC Australian Research Council

• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Depositing User
• Bridget Webb