… induced trees in a graph. By analyzing how FindTree performs in Gn,p, we obtain the following
results. Let T,, be the order of the largest induced … length of the longest induced path in Gn,…

… A tree that is not properly contained in any larger tree is called a maximal tree. Since we
deal here only with induced trees therefore the word 'induced' will be very often omitted. The …

… the random graph G(n, p ) on n vertices with edge probability p = c/n contains almost always
an induced tree … the independence number of a sparse random graph. 0 1996 John Wiley & …

… We consider the size of the largest induced tree in random graphs, random regular graphs
and random regular … 1 -o(l), such graphs have induced trees of size order n. In particular, …

… The problem of the maximum order of an induced tree in a random graph with constant
edge probability was settled by Erd6s and Palka [2] and, independently, by Marchetti-Spaccamela …

… and Pippenger to the induced setting. As corollaries we obtain that … sparse random graph
contains all bounded degree trees of linear order (whp) and that the induced and size induced …

… of determining the size of a largest induced tree in sparse random graphs, when p = d/n for
… (d) > 0 such that whp G(n, p) contains an induced tree of order at least c(d) · n. This problem …

… The problem of existence of large induced trees in random graphs was first studied by of
Erdős and Palka [5]. For a given graph G, with T(G) we denote the size of a largest induced …

… tree sequence of the random graph. Our goal is to study the distribution of t, for a sparse
random … For each model of the random graph, Y( G ) induces a random variable Y. Denote by E,(…

… The second is the Erdös-Renyi random graph model, with … random graphs converge
locally to a rather simple tree model… of unlabeled graphs), we use the topology induced by the …