Edge coloring on graphs #7397
Edge coloring on graphs #7397
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@dschult Could you please check this out ? I've explained our implementation in brief in this conversation. |
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Thanks for this @padath314 and @Sreelaxme (and for the bipartite PR). |
| d + 1 colors. Let u and v be distinct non-adjacent vertices of G. | ||
| Then there exists a proper edge coloring using d + 1 colors | ||
| such that the same color missing at both u and v. | ||
| https://iuuk.mff.cuni.cz/~rakdver/kgii/lesson20-6.pdf |
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Can you make a References section with the full reference to this paper. Links rarely last more than a few years (except for the DOI link to the article). Full reference is more likely to last without additional maintenance.
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We are actually not able to find the DOI link since our reference is a lecture note.
| G = G.copy() | ||
| degrees = dict(G.degree()) | ||
| delta = max(degrees.values()) | ||
| colors = set(range(delta + 1)) |
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Maybe use the range for colors instead of the set.
And make u_colors be the dict used_colors[u] and only use the keys() when doing set operations.
(similar comment to the bipartite version)
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We are keeping the colors as set to make it easier to find available colors using set difference.
This pull request introduces an edge coloring algorithm within the edge_coloring() function. The function now returns a dictionary where each edge is a key, with corresponding values representing the assigned colors.
We have already created a pull request for edge coloring in bipartite graphs (#7138) which gives optimal coloring of bipartite graphs.