An application of maximum-minimum distance circuits on hypercubes

  • Gustavus J. Simmons
Contributed Papers
Part of the Lecture Notes in Mathematics book series (LNM, volume 686)


The related questions of finding Hamilton circuits in the n-dimensional cube with d points on an edge which maximize the minimum "taxicab" distance between successive vertices and/or which maximize the sum of such distances over the entire circuit is investigated. A "good" bound for the first quantity and an achievable limit for the second are developed and several optimal constructions found. Both of these circuits are central to designing pseudo-color graphics displays in which minimal grey scale differences become maximal color differences.


Hamilton Cycle Complete Bipartite Graph Gray Code Adjacent Pair Vertex Pair 
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Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Gustavus J. Simmons
    • 1
  1. 1.Department of Applied MathematicsSandia LaboratoriesAlbuquerqueUSA

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