New results on chromatic index critical graphs

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 ...

Chromatic-index-critical graphs of orders 13 and 14

A graph is chromatic-index-critical if it cannot be edge-coloured with ∆ colours (with ∆ the maximal degree of the graph), and if the removal of any edge decreases its chromatic index. The Critical Graph Conjecture stated that any such graph has odd order. It has been proved false and the smallest known counterexample has order 18 [18, 31]. In this paper we show that there are no chromatic-inde...

Edge Chromatic 5-Critical Graphs

In this paper, we study the structure of 5-critical graphs in terms of their size. In particular, we have obtained bounds for the number of major vertices in several classes of 5-critical graphs, that are stronger than the existing bounds.

On-line 3-chromatic graphs - II critical graphs

On-line coloring of a graph is the following process. The graph is given vertex by vertex (with adjacencies to the previously given vertices) and for the actual vertex a color diierent from the colors of the neighbors must be irrevocably assigned. The on-line chromatic number of a graph G, (G) is the minimum number of colors needed to color on-line the vertices of G (when it is given in the wor...

On the Delta-subgraph of graphs which are critical with respect to the chromatic index