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