Txhua Hamiltonian graphs yog sib txuas, tab sis daim duab sib txuas tsis tas yuav yog Hamiltonian (saib, piv txwv li, Petersen daim duab). Ib daim duab Eulerian G (ib daim duab sib txuas uas txhua qhov vertex muaj txawm tias degree) yuav tsum muaj Euler ncig saib, taug kev kaw hla txhua ntug ntawm G raws nraim ib zaug.
Daim duab puas yog Hamiltonian tab sis tsis yog Eulerian?
Ib daim duab txuas G yog Hamiltonian yog tias muaj lub voj voog uas suav nrog txhua qhov vertex ntawm G; xws li lub voj voog hu ua Hamiltonian cycle. … Daim duab no yog ob qho tib si Eulerian thiab Hamiltonian. Daim duab no yog Eulerian, tab sis tsis yog Hamiltonian. Daim duab no yog Hamiltionian, tab sis tsis yog Eulerian.
Puas yog txhua daim duab Hamiltonian yog Eulerian?
No. Ib txoj hauv Hamiltonian mus ntsib txhua qhov vertex raws nraim ib zaug tab sis tuaj yeem rov ua ntug. Ib lub voj voog Eulerian hla txhua ntug hauv daim duab raws nraim ib zaug tab sis tuaj yeem rov ua qhov vertices.
Eulerian tsis yog Hamiltonian yog dab tsi?
Qhov tiav bipartite graph K2, 4 muaj Eulerian Circuit Court, tab sis tsis yog Hamiltonian (qhov tseeb, nws tsis txawm muaj Hamiltonian txoj kev). Txhua txoj hauv Hamiltonian yuav hloov xim (thiab tsis muaj xiav vertices txaus).
Puas yog tag nrho cov duab Eulerian?
Ib daim duab yog Eulerian yog thiab tsuas yogqib ntawm txhua qhov vertex yog txawm. Yog li ntawd, Kn yog Eulerian yog tias n yog khib. (ii) Tsuas yog ib nrab Eulerian ua tiav daim duab yog K2. … Daim duab txuas nrog, thiab muaj raws nraimob qhov chaw ntawm khib degree.
