Dense critical and vertex-critical graphs

Dense critical and vertex-critical graphs

This paper gives new constructions of k-chromatic critical graphs with high minimum degree and high edge density, and of vertex-critical graphs with high edge density. c © 2002 Elsevier Science B.V. All rights reserved.

Regular vertex diameter critical graphs

A graph is called vertex diameter critical if its diameter increases when any vertex is removed. Regular vertex diameter critical graphs of every valency k ≥ 2 and diameter d ≥ 2 exist, raising the question of identifying the smallest such graphs. We describe an infinite family of k-regular vertex diameter critical graphs of diameter d with at most kd+ (2k − 3) vertices. This improves the previ...

Majority domination vertex critical graphs

This paper deals the graphs for which the removal of any vertex changes the majority domination number of the graph. In the following section, how the removal of a single vertex fromG can change the majority domination number is surveyed for trees. Characterisation of V + M (G) and V − M (G) are determined.

Vertex-splitting and Chromatic Index Critical Graphs

We study graphs which are critical with respect to the chromatic index. We relate these to the Overfull Conjecture and we study in particular their construction from regular graphs by subdividing an edge or by splitting a vertex. In this paper, we consider simple graphs (that is graphs which have no loops or multiple edges). An edge-colouring of a graph G is a map 4 : E(G) -+ cp, where cp is a ...

Vertex Domination Critical in Circulant Graphs