On some Versions of Conjectures of Bondy and Jung

TL;DR

This paper uses algebraic transformations to derive new results related to classical Hamiltonian graph theory conjectures of Bondy and Jung, proposing extended and strengthened versions of these conjectures.

Contribution

It introduces algebraic methods to reformulate and extend well-known Hamiltonian graph theory conjectures, connecting them to classical results.

Findings

New algebraic reformulations of Bondy and Jung conjectures

Extended versions of classical Hamiltonian conjectures proposed

Derivation of new results from earlier work using algebraic transformations

Abstract

Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to well-known conjectures of Bondy and Jung including a number of classical results in hamiltonian graph theory (due to Dirac, Ore, Nash-Williams, Bondy, Jung and so on) as special cases. A number of extended and strengthened versions of these conjectures are proposed.