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Journal of Algebraic Combinatorics

, Volume 2, Issue 1, pp 25–29 | Cite as

Highly Symmetric Subgraphs of Hypercubes

  • A.E. Brouwer
  • I.J. Dejter
  • C. Thomassen
Article

Abstract

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.

edge-coloring hypercube vertex-transitive subgraph 

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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • A.E. Brouwer
    • 1
  • I.J. Dejter
    • 2
  • C. Thomassen
    • 3
  1. 1.Eindhoven Univ. of TechnologyEindhovenNetherlands
  2. 2.Univ. of Puerto RicoRio PiedrasPuerto Rico
  3. 3.Technical Univ. of DenmarkLyngbyDenmark

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