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On the problem of bandsize

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Abstract

We introduce the notion of bandsize (in analogy to bandwidth) as the minimumnumber of edge-differences over all vertex-numberings. We make several observations which allow us to estimate the bandsize of complete binary trees. It follows from our results that the bandsize of the complete binary tree of heightn, n > 10, is betweenc 1 n andc 2 n where 0 <c 1 <c 2 < 1. This is in sharp contrast with the bandwidth of these trees which is roughly\(\frac{{2^n }}{n}\).

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Authors and Affiliations

  1. Department of Mathematics, Simon Fraser University, V5A 156, Burnaby, British Colombia, Canada

    Katherine Heinrich & Pavol Hell

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  1. Katherine Heinrich
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  2. Pavol Hell
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The authors acknowledge the support of N.S.E.R.C. grants U-0165 and A-5075 respectively.

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Heinrich, K., Hell, P. On the problem of bandsize. Graphs and Combinatorics 3, 279–284 (1987). https://doi.org/10.1007/BF01788550

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  • DOI: https://doi.org/10.1007/BF01788550

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