@article{Zhao2024, 
author = {Shenyang Zhao and Fan Wang},
title = {Hamiltonian paths passing through matchings in hypercubes with faulty edges},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {12},
pages = {33692-33711},
keywords = {hypercube, Hamiltonian path, matching, faulty edges},
url = {https://www.sciopen.com/article/10.3934/math.20241608},
doi = {10.3934/math.20241608},
abstract = {Chen considered the existence of a Hamiltonian cycle containing a matching and avoiding some edges in an  n-cube  Qn. In this paper, we considered the existence of a Hamiltonian path and obtained the following result. For  n≥4, let  M be a matching of  Qn, and let  F be a set of edges in  Qn−M with  |M∪F|≤2n−6. Let  x and  y be two vertices of  Qn with different parities satisfying  xy∉M. If all vertices in  Qn−F have a degree of at least  2, then there exists a Hamiltonian path joining  x and  y passing through  M in  Qn−F, with the exception of two cases: (1) there exist two neighbors  v and  t of  x (or  y) satisfying  dQn−F(v)=2 and  xt∈M (or  yt∈M); (2) there exists a path  xvuy of length 3 satisfying  dQn−F(v)=2 and  uy∈M or  dQn−F(u)=2 and  xv∈M.}
}