A localization method in Hamiltonian graph theory

The classical global criteria for the existence of Hamilton cycles only apply to graphs with large edge density and small diameter. In a series papers Asratian Khachatryan developed local in finite connected graphs, which are analogues due Dirac (1952), Ore (1960), Jung (1978), Nash-Williams (1971). idea was show that concept Hamiltonicity can, under rather general conditions, be captured by phenomena, using structure balls radii. (The ball radius $r$ centered at vertex $u$ is subgraph $G$ induced set vertices whose distances from do not exceed $r$.) Such results called localization theorems present possibility extend known classes Hamiltonian graphs. this paper we formulate approach finding use well-known Bauer et al. (1989), Bondy (1980), H\"aggkvist Nicoghossian (1981), Moon Moser (1963). Finally two our infinite locally they guarantee curves, introduced K\"undgen, Li Thomassen (2017).