… The toughness of a graph is an invariant first introduced by Chvatal. In [3] he mainly studied
relations between toughness and the existence of hamiltonian cycles or k-factors, and stated …

In a paper with the same title [3], we proved Chvátal's conjecture thatk-tough graphs havek-factors
if they satisfy trivial necessary conditions. In this paper, we prove the following …

For an undirected graph G, a variation of toughness is defined as τ(G)≔ min |S| w(G−S)−1 w(G−S)⩾2
if G is not complete, and τ(G)≔∞ if G is complete, where w(G−S) is the number of …

… the relations between toughness and the existence of factors of a graph. In this paper, we
consider the relationship between the toughness and the existence of fractional k-factors. It is …

… The toughness of a graph G, denoted by t(G), is defined as the … Chvatal who introduced the
concept of toughness in [2] … G has an f-factor if there exists a spanning subgraph H of G such …

… that ktough graphs have k-factors if they satisfy trivial necessary conditions. In this paper,
we introduce a variation of toughness, and prove a stronger result for the existence of l- or 2-…

… The study of existence of hamiltonian cycles and factors in graphs in terms of toughness was
… In this article, we propose to study toughness conditions for a hypergraph to have a Berge k-…

… ’s result to give a sufficient toughness condition for the existence of m-tree-connected{f,f +
1}-… Moreover, we apply it together with the following recent result to give a sufficient toughness …

… problem of relating toughness to factors … exists a (2 − ϵ)tough graph on at least 3 vertices
having no 2-factor. In recent years, the study of sufficient conditions for graphs with toughness …

… toughness see [2, 13, 14]. In this paper, we show a new result on the relationship between
graph factors and isolated toughness… Then there exist an independent set I and a covering set …