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Hamiltonian graph
Orlovich, Yury L., Gordon, Valery S., Potts, Chris N. and Strusevich, Vitaly A. (2007) On Hamilton cycles in locally connected graphs with vertex degree constraints. Electronic Notes in Discrete Mathematics, 29. pp. 169-173. ISSN 1571-0653 (doi:https://doi.org/10.1016/j.endm.2007.07.028)
local connectivity
Orlovich, Yury L., Gordon, Valery S., Potts, Chris N. and Strusevich, Vitaly A. (2007) On Hamilton cycles in locally connected graphs with vertex degree constraints. Electronic Notes in Discrete Mathematics, 29. pp. 169-173. ISSN 1571-0653 (doi:https://doi.org/10.1016/j.endm.2007.07.028)
NP-completeness
Orlovich, Yury L., Gordon, Valery S., Potts, Chris N. and Strusevich, Vitaly A. (2007) On Hamilton cycles in locally connected graphs with vertex degree constraints. Electronic Notes in Discrete Mathematics, 29. pp. 169-173. ISSN 1571-0653 (doi:https://doi.org/10.1016/j.endm.2007.07.028)