▁kn ight ' s ▁t ours ▁were ▁published ▁by ▁Abraham ▁de ▁Mo iv re ▁and ▁Leon hard ▁E uler . ▁ ▁De fin itions ▁A ▁Hamiltonian ▁path ▁or ▁trace able ▁path ▁is ▁a ▁path ▁that ▁vis its ▁each ▁vertex ▁of ▁the ▁graph ▁exactly ▁once . ▁A ▁graph ▁that ▁contains ▁a ▁Hamiltonian ▁path ▁is ▁called ▁a ▁trace able ▁graph . ▁A ▁graph ▁is ▁Hamiltonian - connected ▁if ▁for ▁every ▁pair ▁of ▁vertices ▁there ▁is ▁a ▁Hamiltonian ▁path ▁between ▁the ▁two ▁vertices . ▁ ▁A ▁Hamiltonian ▁cycle , ▁Hamiltonian ▁circuit , ▁vertex ▁tour ▁or ▁graph ▁cycle ▁is ▁a ▁cycle ▁that ▁vis its ▁each ▁vertex ▁exactly ▁once . ▁A ▁graph ▁that ▁contains ▁a ▁Hamiltonian ▁cycle ▁is ▁called ▁a ▁Hamiltonian ▁graph . ▁ ▁Similar ▁not ions ▁may ▁be ▁defined ▁for ▁directed ▁graphs , ▁where ▁each ▁edge ▁( arc ) ▁of ▁a ▁path ▁or ▁cycle ▁can ▁only ▁be ▁trac ed ▁in ▁a ▁single ▁direction ▁( i . e ., ▁the ▁vertices ▁are ▁connected ▁with ▁ar rows ▁and ▁the ▁edges ▁trac ed ▁" tail - to - head "). ▁ ▁A ▁Hamiltonian ▁decomposition ▁is ▁an ▁edge ▁decomposition ▁of ▁a ▁graph ▁into ▁Hamiltonian ▁circ uits . ▁ ▁A ▁Hamilton ▁ma ze ▁is ▁a ▁type ▁of ▁logic ▁puzz le ▁in ▁which ▁the ▁goal ▁is ▁to ▁find ▁the ▁unique ▁Hamiltonian ▁cycle ▁in ▁a ▁given ▁graph . ▁ ▁Ex amples ▁ ▁a ▁complete ▁graph ▁with ▁more ▁than ▁two ▁vertices ▁is ▁Hamiltonian ▁every ▁cycle ▁graph ▁is ▁Hamiltonian ▁every ▁tournament ▁has ▁an ▁odd ▁number ▁of ▁Hamiltonian ▁paths ▁( R é de i ▁ 1 9