The search session has expired. Please query the service again.

Displaying 901 – 920 of 1341

Showing per page

On the existence of a cycle of length at least 7 in a (1,≤ 2)-twin-free graph

David Auger, Irène Charon, Olivier Hudry, Antoine Lobstein (2010)

Discussiones Mathematicae Graph Theory

We consider a simple, undirected graph G. The ball of a subset Y of vertices in G is the set of vertices in G at distance at most one from a vertex in Y. Assuming that the balls of all subsets of at most two vertices in G are distinct, we prove that G admits a cycle with length at least 7.

On the Existence of (k,l)-Kernels in Infinite Digraphs: A Survey

H. Galeana-Sánchez, C. Hernández-Cruz (2014)

Discussiones Mathematicae Graph Theory

Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A (k, l)-kernel N of D is a k-independent (if u, v ∈ N, u 6= v, then d(u, v), d(v, u) ≥ k) and l-absorbent (if u ∈ V (D) − N then there exists v ∈ N such that d(u, v) ≤ l) set of vertices. A k-kernel is a (k, k −1)-kernel. This work is a survey of results proving sufficient conditions for the existence of (k, l)-kernels in infinite digraphs. Despite all the previous work in this direction was done for...

Currently displaying 901 – 920 of 1341