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Graph homomorphisms through random walks [electronic resource]

Daneshgar, A. (Amir) ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1002/jgt.10125
  3. Abstract:
  4. In this paper we introduce some general necessary conditions for the existence of graph homomorphisms, which hold in both directed and undirected cases. Our method is a combination of Diaconis and Saloff–Coste comparison technique for Markov chains and a generalization of Haemers interlacing theorem. As some applications, we obtain a necessary condition for the spanning subgraph problem, which also provides a generalization of a theorem of Mohar (1992) as a necessary condition for Hamiltonicity. In particular, in the case that the range is a Cayley graph or an edge-transitive graph, we obtain theorems with a corollary about the existence of homomorphisms to cycles. This, specially, provides a proof of the fact that the Coxeter graph is a core. Also, we obtain some information about the cores of vertex-transitive graphs
  5. Keywords:
  6. Graph colouring ; Graph homomorphism ; Graph spectra ; Markov chains
  7. Source: Journal of Graph Theory ; 2003, Volume 44, Issue 1, pages 15–38
  8. URL: http://onlinelibrary.wiley.com/doi/10.1002/jgt.10125/abstract;jsessionid=C7E1466728E55B99EA600AC005ADE77F.f03t02?systemMessage=Wiley+Online+Library+will+be+disrupted+9th+Aug+from+10-2+BST+for+essential+maintenance.+Pay+Per+View+will+be+unavailable+from+10-6+BST