Toughness, hamiltonicity and split graphs

  title={Toughness, hamiltonicity and split graphs},
  author={Dieter Kratsch and Jen{\"o} Lehel and Haiko M{\"u}ller},
  journal={Discret. Math.},

Figures from this paper

On Toughness and Hamiltonicity of 2K2‐Free Graphs
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.
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
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
Toughness and hamiltonicity in k-trees
Hamiltonian powers in threshold and arborescent comparability graphs
Toughness, 2-factors and Hamiltonian cycles in 2K2-free graphs
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.
Hamiltonian cycles in 7-tough (P3 ∪ 2P1)-free graphs
Toughness, Forbidden Subgraphs and Pancyclicity
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
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
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


Tough graphs and hamiltonian circuits
Finding Hamiltonian paths in cocomparability graphs using the bump number algorithm
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
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.
Hamiltonian Cycle is Polynomial on Cocomparability Graphs
Toughness and the existence of k-factors
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.
Toughness, minimum degree, and the existence of 2-factors
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]
Finding Hamiltonian Circuits in Interval Graphs
  • J. Keil
  • Mathematics
    Inf. Process. Lett.
  • 1985
Two sufficient conditions for a 2-factor in a bipartite graph
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.