Bounds on the convex label number of trees

Combinatorica volume 7, pages221–230(1987)Cite this article

Abstract

A convex labelling of a tree is an assignment of distinct non-negative integer labels to vertices such that wheneverx, y andz are the labels of vertices on a path of length 2 theny≦(x+z)/2. In addition if the tree is rooted, a convex labelling must assign 0 to the root. The convex label number of a treeT is the smallest integerm such thatT has a convex labelling with no label greater thanm. We prove that every rooted tree (and hence every tree) withn vertices has convex label number less than 4n. We also exhibitn-vertex trees with convex label number 4n/3+o(n), andn-vertex rooted trees with convex label number 2n +o(n).

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Author information

Affiliations

  1. Computer Science Division, U. C. Berkeley, 94720, Berkeley, CA, USA

    Marshall Bern & Alice Wong

  2. IBM Almaden Research Center, K53/802, 650 Haury Rd., 95120, San Jose, CA, USA

    Maria Klawe

Authors
  1. Marshall Bern
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  2. Alice Wong
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  3. Maria Klawe
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Additional information

The research by M. B. and A. W. was partly supported by NSF grant MCS—8311422.

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Bern, M., Wong, A. & Klawe, M. Bounds on the convex label number of trees. Combinatorica 7, 221–230 (1987). https://doi.org/10.1007/BF02579299

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