On the treewidth and related parameters of random geometric graphs

Dieter Mitsche , Guillem Perarnau (1)

1 UPC - Universitat Politècnica de Catalunya = Université polytechnique de Catalogne [Barcelona]

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.

Mots clés: Random geometric graphs; treewidth; treedepth

Domaines: Complexité [cs.CC]; Algorithme et structure de données [cs.DS]

Dieter Mitsche, Guillem Perarnau. On the treewidth and related parameters of random geometric graphs. STACS'12 (29th Symposium on Theoretical Aspects of Computer Science), Feb 2012, Paris, France. pp.408-419. ⟨hal-00678199⟩