isomorphic factorization - Wolfram|Alpha

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Input interpretation

isomorphic factorization

Definition

Isomorphic factorization colors the edges a given graph G with k colors so that the colored subgraphs are isomorphic. The graph G is then k-splittable, with k as the divisor, and the subgraph as the factor.
When a complete graph is 2-split, a self-complementary graph results. Similarly, an n-regular class 1 graph can be n-split into graphs consisting of disconnected edges, making n the edge chromatic number.
The complete graph K_9 can be 3-split into identical planar graphs.

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Related terms

complete graph | edge coloring | isomorphic graphs

Subject classifications

MathWorld

graph coloring | Ramsey theory | miscellaneous graphs | unsolved problems

MSC 2010

05C15 | 05Cxx | 05D10

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