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On the treewidth and related parameters of random geometric graphs

Authors Dieter Mitsche, Guillem Perarnau



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LIPIcs.STACS.2012.408.pdf
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Dieter Mitsche
Guillem Perarnau

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Dieter Mitsche and Guillem Perarnau. On the treewidth and related parameters of random geometric graphs. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 408-419, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2012)
https://doi.org/10.4230/LIPIcs.STACS.2012.408

Abstract

We give asymptotically exact values for the treewidth tw(G) of a random geometric graph G(n,r) in [0,sqrt(n)]^2. More precisely, we show that there exists some c_1 > 0, such that for any constant 0 < r < c_1, tw(G)=Theta(log(n)/loglog(n)), and also, there exists some c_2 > c_1, such that for any r=r(n)> c_2, tw(G)=Theta(r sqrt(n)). Our proofs show that for the corresponding values of r the same asymptotic bounds also hold for the pathwidth and treedepth of a random geometric graph.
Keywords
  • Random geometric graphs
  • treewidth
  • treedepth

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