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On the diameter of random planar graphs
(2015)
Article
Open AccessWe show that the diameter diam(Gn) of a random labelled connected planar graph with n vertices is equal to n1/4+o(1) , in probability. More precisely, there exists a constant c > 0 such that {equation presented} for ˜ small ... 
Grouptheoretic orbit decidability
(De Gruytr, 20141201)
Article
Restricted access  publisher's policyA recent collection of papers in the last years have given a renovated interest to the notion of orbit decidability. This is a new quite general algorithmic notion, connecting with several classical results, and closely ... 
An involution on bicubic maps and beta(0,1)trees
(2015)
Article
Open AccessBicubic maps are in bijection with (0 ; 1)trees. We introduce two new ways of decomposing (0 ; 1)trees. Using this we de ne an endofunc tion on (0 ; 1)trees, and thus also on bicubic maps. We show that ... 
Fixed subgroups in free groups: a survey
(200203)
Article
Open AccessThis note is a survey of the main results known about fixed subgroups of endomorphisms of finitely generated free groups. A historic point of view is taken, emphasizing the evolution of this line of research, from ... 
On automorphismfixed subgroups of a free group
(200008)
Article
Open AccessLet F be a flnitely generated free group, and let n denote its rank. A subgroup H of F is said to be automorphismflxed, or autoflxed for short, if there exists a set S of automorphisms of F such that H is precisely the ... 
Twisted conjugacy in braid groups
(20140101)
Article
Open AccessIn this note we solve the twisted conjugacy problem for braid groups, i.e., we propose an algorithm which, given two braids u,v is an element of Bn and an automorphism phi is an element of Aut(Bn), decides whether v = ... 
A description of autofixed subgroups in a free group
(200406)
Article
Open AccessLet F be a finitely generated free group. By using BestvinaHandel theory, as well as some further improvements, the eigengroups of a given automorphism of F (and its fixed subgroup among them) are globally analyzed and ... 
Statistical properties of subgroups of free groups
(20130204)
Article
Open AccessThe usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the socalled wordbased distribution: subgroups are generated ... 
A Whitehad algorithm for toral relatively hyperbolic groups
(20121204)
Article
Open AccessThe Whitehead problem is solved in the class of toral relatively hyperbolic groups G (i.e. torsionfree relatively hyperbolic groups with abelian parabolic subgroups): there is an algorithm which, given two nite ... 
The conjugacy problem in automaton groups is not solvable
(20120815)
Article
Open Access(Free abelian)byfree, selfsimilar groups generated by finite selfsimilar sets of tree automorphisms and having unsolvable conjugacy problem are constructed. Along the way, finitely generated, orbit undecidable, free ...