Linked from

The 15 pages that link to Edge coloring, each with the reason it gives.

• Graph coloringCompared with: It colors edges rather than vertices, modeling conflicts at shared endpoints.

• Ramsey theoryRelated: The basic finite Ramsey problem asks what colored edges force.

• Chromatic numberCompared with: It colors edges rather than vertices, so its minimum is a different graph invariant.

• Line graphRelated: Edge coloring becomes vertex coloring of the line graph.

• Petersen graphNarrower topic: The Petersen graph’s failure of 3-edge-colorability is central to its reputation.

• Chromatic polynomialCompared with: It colors edges rather than vertices, so its counting polynomial captures a different constraint.

• Vizing's theoremNarrower topic: Vizing’s theorem bounds the number of colors needed for this graph-coloring problem.

• Kőnig's theoremRelated: Bipartite edge-coloring results use repeated matchings as color classes.

• Edge coverCompared with: Edge coloring organizes conflicts among edges instead of covering vertices.

• Erdős–Faber–Lovász conjectureRelated: Coloring the hyperedges is the same as coloring vertices of their line graph.

• Burr–Erdős conjectureRelated: Monochromatic copies in edge-colorings define the Ramsey numbers at issue.

• Dinitz theoremRelated: Treating cells as edges turns the array condition into a proper edge-coloring condition.

• Friends and strangers theoremRelated: Coloring each pair by relationship type turns the claim into a two-color graph problem.

• Goldberg–Seymour conjectureNarrower topic: The conjecture bounds the minimum number of colors needed for this assignment.

• List coloring conjectureNarrower topic: Its minimum color count is the ordinary parameter the conjecture compares.