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Packing Chromatic Number of Base-3 Sierpiński Graphs

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Abstract

The packing chromatic number \(\chi _{\rho }(G)\) of a graph G is the smallest integer k such that there exists a k-vertex coloring of G in which any two vertices receiving color i are at distance at least \(i+1\). Let \(S^n\) be the base-3 Sierpiński graph of dimension n. It is proved that \(\chi _{\rho }(S^1) = 3\), \(\chi _{\rho }(S^2) = 5\), \(\chi _{\rho }(S^3) = \chi _{\rho }(S^4) = 7\), and that \(8\le \chi _\rho (S^n) \le 9\) holds for any \(n\ge 5\).

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Authors and Affiliations

  1. Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia

    Boštjan Brešar & Sandi Klavžar

  2. Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia

    Boštjan Brešar & Sandi Klavžar

  3. Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia

    Sandi Klavžar

  4. Department of Mathematics, Furman University, Greenville, SC, USA

    Douglas F. Rall

Authors
  1. Boštjan Brešar
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  2. Sandi Klavžar
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  3. Douglas F. Rall
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Correspondence to Boštjan Brešar.

Additional information

B.B. and S.K. supported in part by the Slovenian research agency (ARRS) under the Grant P1-0297. D.F.R. supported by a grant from the Simons Foundation (Grant Number 209654 to Douglas F. Rall).

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Brešar, B., Klavžar, S. & Rall, D.F. Packing Chromatic Number of Base-3 Sierpiński Graphs. Graphs and Combinatorics 32, 1313–1327 (2016). https://doi.org/10.1007/s00373-015-1647-x

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  • DOI: https://doi.org/10.1007/s00373-015-1647-x

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