## 56 Citations

On Toughness and Hamiltonicity of 2K2‐Free Graphs

- MathematicsJ. Graph Theory
- 2014

It is proved that the problem of determining toughness is polynomially solvable and that Chvatal's toughness conjecture is true for 2K2-free graphs.

Toughness and Hamiltonicity in Random Apollonian Networks.

- Mathematics
- 2020

In this paper we study the toughness of Random Apollonian Networks (RANs), a random graph model which generates planar graphs with power-law properties. We consider their important characteristics:…

Hamiltonian cycles in tough (P2 ∪ P3)-free graphs

- Mathematics
- 2021

Let t > 0 be a real number and G be a graph. We say G is t-tough if for every cutset S of G, the ratio of |S| to the number of components of G− S is at least t. Determining toughness is an NP-hard…

Hamiltonian powers in threshold and arborescent comparability graphs

- MathematicsDiscret. Math.
- 1999

Toughness, 2-factors and Hamiltonian cycles in 2K2-free graphs

- Mathematics
- 2021

A graph G is called a 2K2-free graph if it does not contain 2K2 as an induced subgraph. In 2014, Broersma et al. showed that every 25-tough 2K2-free graph with at least three vertices is Hamiltonian.…

Toughness, Forbidden Subgraphs and Pancyclicity

- MathematicsGraphs Comb.
- 2021

It is found that the results are completely analogous to the hamiltonian case: every graph H such that any 1-tough H-free graph is hamiltonia also ensures that every 1-magnifying H- free graph is pancyclic, except for a few specific classes of graphs.

Toughness, Forbidden Subgraphs, and Hamilton-Connected Graphs

- MathematicsDiscuss. Math. Graph Theory
- 2022

All possible forbidden subgraphs H such that every H-free graph G with τ (G) > 1 is Hamilton-connected are investigated, and it is found that the results are completely analogous to the Hamiltonian case.

Hamiltonian cycles in 2-tough $2K_2$-free graphs

- Mathematics
- 2021

A graph G is called a 2K2-free graph if it does not contain 2K2 as an induced subgraph. In 2014, Broersma, Patel and Pyatkin showed that every 25-tough 2K2free graph on at least three vertices is…

## References

SHOWING 1-10 OF 32 REFERENCES

Finding Hamiltonian paths in cocomparability graphs using the bump number algorithm

- Mathematics
- 1991

Hamiltonian Path/Cycle are well known NP-complete problems on general graphs, but their complexity status for permutation graphs has been an open question in algorithmic graph theory for many years.…

Polynomial Algorithms for Hamiltonian Cycle in Cocomparability Graphs

- MathematicsSIAM J. Comput.
- 1994

It is shown that the Hamiltonian cycle existence problem for cocomparability graphs is in $P$ and a polynomial time algorithm for constructing a Hamiltonian path and cycle is presented.

Toughness and the existence of k-factors

- MathematicsJ. Graph Theory
- 1985

For any positive integer k and for any positive real number e, there exists a (k - e)-tough graph G with k|G| even and |G| ⩾ k + 1 which has no k-factor.

Linear time algorithms for NP-hard problems restricted to partial k-trees

- Mathematics, Computer ScienceDiscret. Appl. Math.
- 1989

Toughness, minimum degree, and the existence of 2-factors

- MathematicsJ. Graph Theory
- 1994

Degree conditions on the vertices of a t-tough graph G(1 ≦ t ≦ 2) that ensure the existence of a 2-factor in G are presented. These conditions are asymptotically best possible for every t ϵ [1, 3/2]…

Two sufficient conditions for a 2-factor in a bipartite graph

- MathematicsJ. Graph Theory
- 1987

It is proved that every 1-tough bipartite graph which is not isomorphic to K1,1 has a 2-factor, and a sufficient condition for the existence of a2-factor in a bipartites graph is obtained in the spirit of Hall's theorem.