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Rigidity and Separation Indices of Graphs in Surfaces

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Abstract

Let Σ be a surface. We prove that rigidity indices of graphs which admit a polyhedral embedding in Σ and 5-connected graphs admitting an embedding in Σ are bounded by a constant depending on Σ. Moreover if the Euler characteristic of Σ is negative, then the separation index of graphs admitting a polyhedral embedding in Σ is also bounded. As a side result we show that distinguishing number of both Σ-polyhedral and 5-connected graphs which admit and embedding in Σ is also bounded.

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Authors and Affiliations

  1. Faculty of Computer and Information Science, University of Ljubljana, Ljubljana, Slovenia

    Gašper Fijavž

  2. Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada

    Bojan Mohar

Authors
  1. Gašper Fijavž
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  2. Bojan Mohar
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Corresponding author

Correspondence to Gašper Fijavž.

Additional information

G. Fijavž was supported in part by the Research Grant P1-0297 of ARRS (Slovenia).

B. Mohar was supported in part by an NSERC Discovery Grant (Canada), by the Canada Research Chair Program, and by the Research Grant P1-0297 of ARRS (Slovenia).

B. Mohar is on leave from IMFM & FMF, Department of Mathematics, University of Ljubljana, Ljubljana, Slovenia.

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Fijavž, G., Mohar, B. Rigidity and Separation Indices of Graphs in Surfaces. Graphs and Combinatorics 26, 491–498 (2010). https://doi.org/10.1007/s00373-010-0929-6

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  • DOI: https://doi.org/10.1007/s00373-010-0929-6

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