Abstract
An example of such a theorem is the well-known Chvátal–Erdős Theorem, which states that every graph G with ακ is hamiltonian. Here κ is the vertex connectivity of G and α is the cardinality of a largest set of independent vertices of G. In another paper Chvátal points out that the proof of this result is in fact a polynomial time construction that either produces a Hamilton cycle or a set of more than κ independent vertices. In this note we point out that other theorems in hamiltonian graph theory have a similar character. In particular, we present a constructive proof of a well-known theorem of Jung (Ann. Discrete Math. 3 (1978) 129) for graphs on 16 or more vertices.
Original language | English |
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Pages (from-to) | 13-23 |
Number of pages | 11 |
Journal | Discrete applied mathematics |
Volume | 120 |
Issue number | 1-3 |
DOIs | |
Publication status | Published - 2002 |
Keywords
- NP-hardness
- Hamiltonian graphs
- Toughness
- Constructive proofs
- Complexity
- Polynomial algorithms