The critical window in random digraphs Page 1 Combinatorics, Probability and Computing (2022),
31, pp. 411–429 doi:10.1017/S096354832100033X ARTICLE The critical window in random …

An n‐state deterministic finite automaton over ak‐letter alphabet can be seen as a digraph
with n vertices which all have k labeled out‐arcs. Grusho (Publ Math Inst Hungarian Acad …

Many references to date on the enumeration of graphs deal with unlabelled graphs, like the
monographs of Harary and Palmer [36] and Pólya and Read [57]. The main tool there is the …

Random trees are ubiquitous in computer science. One particularly attractive model is the
random tree chosen uniformly from a collection of trees. Many of these models are …

We obtain exact expressions counting the satisfiable 2-SAT formulae and describe the
structure of associated implication digraphs. Our approach is based on generating function …

Two models of a random digraph on n vertices, and are studied. In 1990, Karp for D (n, p)
and independently T. Łuczak for D (n, m= cn) proved that for c> 1, with probability tending to …

A sharp asymptotic formula for the number of strongly connected digraphs on n labelled
vertices with m arcs, under the condition m‐n≫ n2/3, m= O (n), is obtained; this provides a …

Abstract The (k 1, k 2)-core of a digraph is the largest sub-digraph with minimum in-degree
and minimum out-degree at least k 1 and k 2 respectively. For max⁡{k 1, k 2}≥ 2, we …

We study the behaviour of the largest components of the directed configuration model in the
barely subcritical regime. We show that with high probability all strongly connected …

References........................................................... 4326.1 Introduction Many references to date on
the enumeration of graphs deal with unlabeled graphs, like the monographs of Harary and …