Add to ORKGIn graph theory, the term critical is usually used with respect to specified graph parameter P and applies when the graph G under consideration has the property P but alteration of G (such as vertex deletion, edge deletion or edge addition) result in a graph not having property P. In this paper, we consider graphs which are critical with respect to parameter P under the single operation of: deleting a vertex; deleting an edge; adding an edge. In particular, we focus on the graph parameters: diameter, connectivity and edge-connectivity. We review important results and mention many open problems
AbstractA graph is called a split graph if its vertex set can be partitioned into a clique and an in...
International audienceThe k-restricted edge-connectivity of a graph G, denoted by λ k (G), is define...
A graph is diameter two edge-critical if its diameter is two and the deletion of any edge increases ...
In graph theory, the term critical is usually used with respect to specified graph parameter P and ...
AbstractA diameter critical graph has the property that the addition of any edge decreases the diame...
AbstractA graph is diameter 2-critical if the graph has diameter 2 and the deletion of any edge incr...
AbstractA graph is vertex-critical if deleting any vertex increases its diameter. We construct, for ...
<p>A graph is called diameter-k-critical if its diameter is k, and the removal of any edge strictly ...
All digraphs are determined that have the property that when any vertex and any edge that are not ad...
AbstractA simple connected graph G with diam(G) = d is said to be ‘vertex diameter-d-critical’ if di...
A vertex or edge in a graph is critical if its deletion reduces the chromatic number of the graph by...
Thesis (Ph.D.), Department of Mathematics, Washington State UniversityA graph G is alpha-critical (o...
AbstractA graph G is diameter k-critical if the graph has diameter k and the deletion of any edge in...
We define a graph G=(V, E) with m=\E\ edges, n=\V\ vertices, maximum degree D, and diameter d, to b...
AbstractSumner and Blitch defined a graph G to be k-y-critical if y(G) = k and y(G + uv) = k - 1 for...
AbstractA graph is called a split graph if its vertex set can be partitioned into a clique and an in...
International audienceThe k-restricted edge-connectivity of a graph G, denoted by λ k (G), is define...
A graph is diameter two edge-critical if its diameter is two and the deletion of any edge increases ...
In graph theory, the term critical is usually used with respect to specified graph parameter P and ...
AbstractA diameter critical graph has the property that the addition of any edge decreases the diame...
AbstractA graph is diameter 2-critical if the graph has diameter 2 and the deletion of any edge incr...
AbstractA graph is vertex-critical if deleting any vertex increases its diameter. We construct, for ...
<p>A graph is called diameter-k-critical if its diameter is k, and the removal of any edge strictly ...
All digraphs are determined that have the property that when any vertex and any edge that are not ad...
AbstractA simple connected graph G with diam(G) = d is said to be ‘vertex diameter-d-critical’ if di...
A vertex or edge in a graph is critical if its deletion reduces the chromatic number of the graph by...
Thesis (Ph.D.), Department of Mathematics, Washington State UniversityA graph G is alpha-critical (o...
AbstractA graph G is diameter k-critical if the graph has diameter k and the deletion of any edge in...
We define a graph G=(V, E) with m=\E\ edges, n=\V\ vertices, maximum degree D, and diameter d, to b...
AbstractSumner and Blitch defined a graph G to be k-y-critical if y(G) = k and y(G + uv) = k - 1 for...
AbstractA graph is called a split graph if its vertex set can be partitioned into a clique and an in...
International audienceThe k-restricted edge-connectivity of a graph G, denoted by λ k (G), is define...
A graph is diameter two edge-critical if its diameter is two and the deletion of any edge increases ...