2 research outputs found
Hamiltonicity of locally hamiltonian and locally traceable graphs
Please read abstract in the article.The University of South Africa and the National Research Foundation of South Africa for their sponsorship of the Salt Rock Workshops of 28 July–10 August 2013 and 20–30 January 2016, which contributed towards results in this paper.
The authors thank the DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) for financial support, grant number BA2017/268. Opinions expressed and conclusions arrived at are those of the authors and are not necessarily to be attributed to the CoE-MaSS.
This material is based upon the third author’s work supported by the National Research Foundation of S.A. under Grant number 81075 and the second author’s work supported by the National Research Foundation of S.A. under Grant number 107668.http://www.elsevier.com/locate/dam2019-02-19hj2018Mathematics and Applied Mathematic
Some local--global phenomena in locally finite graphs
In this paper we present some results for a connected infinite graph with
finite degrees where the properties of balls of small radii guarantee the
existence of some Hamiltonian and connectivity properties of . (For a vertex
of a graph the ball of radius centered at is the subgraph of
induced by the set of vertices whose distance from does not
exceed ). In particular, we prove that if every ball of radius 2 in is
2-connected and satisfies the condition for
each path in , where and are non-adjacent vertices, then
has a Hamiltonian curve, introduced by K\"undgen, Li and Thomassen (2017).
Furthermore, we prove that if every ball of radius 1 in satisfies Ore's
condition (1960) then all balls of any radius in are Hamiltonian.Comment: 18 pages, 6 figures; journal accepted versio