On the maximal number of independent circuits in a graph

Sufficient Condition for the Existence of Three Disjoint Theta Graphs

“…Pósa [9] proved that any graph with minimum degree at least three contains a chorded cycle. Motivated by these results, Finkel et al [6] and Chiba et al [3] obtained the following results analogous to Theorem 1.2, respectively.…”

“…Corrádi and Hajnal [3] proved the following well-known result on the existence of vertex-disjoint cycles in graphs.…”

How Tight is the Corner Relaxation? Insights Gained from the Stable Set Problem

“…Under this assumption, applying Theorem 5.1 with k = 1, it follows that z corner(B) = n−1 2 , if n is odd, and z corner(B) = n 2 if n is even. A sufficient condition for V to be partitioned into triangles is established by [15] and amounts to requiring that the minimum vertex degree is at least 2 3 n. A random graph G(n, p) almost surely has such a partition whenever n = 3k and p ≥ O(…”

On maximum cycle packings in polyhedral graphs

“…A large amount of literature can be found concerning conditions that are sufficient for the existence of some number of disjoint cycles which may satisfy further restrictive conditions. For examples, we refer to publications [6], [9], [10], [12], [15], [16], [18], [20], [21], [23], [24]. The algorithmic problems concerning cycle packings are typically hard ( [5], [11], [20]) and approximation algorithms are described ( [11], [17]).…”