Talk:Edge coloring

"The" objective?

I'm uncomfortable with talking about the objective in the third sentence of the intro. That is certainly one possible objective. But other objectives for edge colorings (particularly when dealing with complete graphs) are common, for example, in Ramsey theory you might wish to avoid monochromatic triangles (or other larger complete monochromatic subgraphs) or other monochromatic graphs in the case of Graph Ramsey Theory. At least for beginning of the intro, the notion of an edge coloring should be just that, an arbitrary edge coloring of the graph. Later, we can specialize to whatever additional conditions that we might wish to put on those edge colorings. --Ramsey2006 (talk) 06:43, 19 August 2008 (UTC)[reply]

Errors?

-- Additional properties --

with the property that there exists a proper edge coloring of a given graph G with m1 edges of the first color, m2 edges of the first color, etc.

Maybe

first color, m2 edges of the second color, etc.

-- Other types of edge coloring --

a proper edge coloring in which each pair of colors must be represented by at least one pair of adjacent edges.

Edges? According to article Complete coloring

every pair of colors appears on at least one pair of adjacent vertices.Jumpow (talk) 19:31, 29 November 2013 (UTC)Jumpow[reply]