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Title:
On Some Versions of Conjectures of Bondy and Jung
Other title:
Բոնդիի և Յունգի վարկածների որոշ տարբերակների մասին; О некоторых версиях гипотез Бонди и Юнга
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Hamilton cycle ; Dominating cycle ; Long cycles ; Bondy's conjecture ; Jung's Conjecture
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Abstract:
Most known fundamental theorems in hamiltonian graph theory (due to Dirac, Ore, Nash-Williams, Bondy, Jung and so on) are related to the length p of a longest cycle C in a graph G in terms of connectivity k and the length p of a longest path in G-C, for the special cases when k≤3 and p≤1 (if p = -1 then V(G-C)=ø and C is called hamiltonian; and if p = 0 then V(G-C) is an independent set of vertices and C is called dominating). Bondy (1980) and Jung (2001) conjectured a common generalization of these results in terms of degree sums including p and k as parameters.