Geodesic
Highly symmetric subgraphs of hypercubes
Journal of Algebraic Combinatorics, Tome 2 (1993) no. 1, pp. 25-29.

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Summary: Two questions are considered, namely (i) How many colors are needed for a coloring of the $n$-cube without monochromatic quadrangles or hexagons? We show that four colors suffice and thereby settle a problem of Erdös. (ii) Which vertex-transitive induced subgraphs does a hypercube have? An interesting graph has come up in this context: If we delete a Hamming code from the 7-cube, the resulting graph is 6-regular, vertex-transitive and its edges can be two-colored such that the two monochromatic subgraphs are isomorphic, cubic, edge-transitive, nonvertex-transitive graphs of girth 10.
Keywords: edge-coloring, hypercube, vertex-transitive subgraph 
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     title = {Highly symmetric subgraphs of hypercubes},
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Brouwer, A.E.; Dejter, I.J.; Thomassen, C. Highly symmetric subgraphs of hypercubes. Journal of Algebraic Combinatorics, Tome 2 (1993) no. 1, pp. 25-29. http://geodesic.mathdoc.fr/item/JAC_1993__2_1_a4/