2022/03/25 by Du, Shaofei, Tian, Yao, Yu, Hao · 2 citations
#05C25 #05C45 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2203.13460
After long term efforts, it was recently proved in \citeDKM2 that except for the Peterson graph, every connected vertex-transitive graph of order rs has a Hamilton cycle, where r and s are primes. A natural topic is to solve the hamiltonian problem for connected vertex-transitive graphs of 2rs. This topic is quite trivial, as the problem is still unsolved even for that of r=3. In this paper, it is shown that except for the Coxeter graph, every connected vertex-transitive graph of order 2rs contains a Hamilton cycle, provided the automorphism group acts primitively on vertices.