| Popis: |
Ciklična svežnjevska Hamiltonskost cbH(G) grafa G je najmanjši n, za katerega obstaja tak avtomorfizem grafa G, da je kartezični grafovski sveženj, katerega baza je cikel na n točkah in vlakno graf G, Hamiltonov graf. Podamo oceno za cbH(G) in to oceno dokažemo. Podamo potrebne in zadostne pogoje za povezanost direktnih grafovskih svežnjev katerih vlakna so cikli. Pokažemo tudi, da so vsi povezani direktni grafovski svežnji ciklov nad cikli Hamiltonovi grafi. Cyclic bundle Hamiltonicity cbH(G) is the minimal n for which there is an automorphism of G such that the Cartesian graph bundle with cycle as base and G as fiber is Hamiltonian. We prove the value of cbH(G). A necessary and sufficient condition for connectedness of direct graph bundles where the fibers are cycles is given. It is also proved that all connected direct graph bundles cycles over cycles are Hamiltonian. |
