Displaying similar documents to “On the structure of the point arboricity critical graphs”

Generalized matrix graphs and completely independent critical cliques in any dimension

John J. Lattanzio, Quan Zheng (2012)

Discussiones Mathematicae Graph Theory

Similarity:

For natural numbers k and n, where 2 ≤ k ≤ n, the vertices of a graph are labeled using the elements of the k-fold Cartesian product Iₙ × Iₙ × ... × Iₙ. Two particular graph constructions will be given and the graphs so constructed are called generalized matrix graphs. Properties of generalized matrix graphs are determined and their application to completely independent critical cliques is investigated. It is shown that there exists a vertex critical graph which admits a family of k...

A characterization of diameter-2-critical graphs with no antihole of length four

Teresa Haynes, Michael Henning (2012)

Open Mathematics

Similarity:

A graph G is diameter-2-critical if its diameter is two and the deletion of any edge increases the diameter. In this paper we characterize the diameter-2-critical graphs with no antihole of length four, that is, the diameter-2-critical graphs whose complements have no induced 4-cycle. Murty and Simon conjectured that the number of edges in a diameter-2-critical graph of order n is at most n 2/4 and that the extremal graphs are complete bipartite graphs with equal size partite sets. As...