Tough graphs and hamiltonian circuits

@article{Chvtal1973ToughGA,
  title={Tough graphs and hamiltonian circuits},
  author={V. Chv{\'a}tal},
  journal={Discret. Math.},
  year={1973},
  volume={5},
  pages={215-228}
}
  • V. Chvátal
  • Published 1973
  • Computer Science, Mathematics
  • Discret. Math.
The toughness of a graph G is defined as the largest real number t such that deletion of any s points from G results in a graph which is either connected or else has at most s/t components. Clearly, every hamiltonian graph is 1-tough. Conversely, we conjecture that for some t"0, every t"0-tough graph is hamiltonian. Since a square of a k-connected graph is always k-tough, a proof of this conjecture with t"0 = 2 would imply Fleischner's theorem (the square of a block is hamiltonian). We… Expand
374 Citations
Toughness of graphs and the existence of factors
  • 32
  • PDF
Hamiltonian cycles in tough (P2 ∪ P3)-free graphs
  • Highly Influenced
On Path-Tough Graphs
  • 12
  • Highly Influenced
Tough Ramsey Graphs Without Short Cycles
  • 37
  • PDF
A Remark on Hamiltonian Cycles
  • 3
Toughness, trees, and walks
  • 34
  • PDF
Toughness, trees, and walks
  • 15
On the toughness index of planar graphs
  • 8
Toughness, hamiltonicity and split graphs
  • 49
  • Highly Influenced
  • PDF
Toughness, Forbidden Subgraphs, and Hamilton-Connected Graphs
  • Highly Influenced
  • PDF
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 17 REFERENCES
Pancyclic graphs II
  • 206
A note on Hamiltonian circuits
  • 519
  • PDF
A short proof of the factor theorem for finite graphs
  • 257
  • PDF
Congruent Graphs and the Connectivity of Graphs
  • 964
Graphs and subgraphs
  • 33
  • PDF
Existence of k-edge connected ordinary graphs with prescribed degrees
  • 45
  • PDF
On Hamilton's ideals
  • 249
On colouring the nodes of a network
  • 260
Graph theory
  • 13,766
  • PDF
Properties of graphs with constraints on degrees
  • Studia Sci. Math. Hung. 4
  • 1969
...
1
2
...