Skip to main content
1 of 1
Post Made Community Wiki

I do not think that edge-coloring is necessarily less interesting than vertex-coloring. I work in neither but have used both in my research. I have a feeling that vertex-coloring may be perceived as more important in general graph theory, where the object of the study are graphs not necessarily with some particular structure and colorings are closely related to graph morphisms. Vertex color classes are independent sets, while edge-color classes are matchings. I found both concepts very useful.

However if the coloring is considered as part of the structure, it is hard to tell which concept is more popular. For instance, incidence geometries may be viewed as graphs with a given vertex-coloring. On the other hand, say, a Cayley graph is a graph that carries a natural edge-coloring structure.