On the growth of components with non fixed excesses

Anne-Elisabeth Baert (1) , Vlady Ravelomanana (2) , Loÿs Thimonier (1)

1 LaRIA - Laboratoire de Recherche en Informatique d'Amiens
2 LIPN - Laboratoire d'Informatique de Paris-Nord

Denote by an $l$-component a connected graph with $l$ edges more than vertices. We prove that the expected number of creations of $(l+1)$-component, by means of adding a new edge to an $l$-component in a randomly growing graph with $n$ vertices, tends to $1$ as $l,n$ tends to $\infty$ but with $l = o(n^{1/4})$. We also show, under the same conditions on $l$ and $n$, that the expected number of vertices that ever belong to an $l$-component is $\sim (12l)^{1/3} n^{2/3}$.

Mots clés: Random graphs; Analytic combinatorics; Giant components

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

Anne-Elisabeth Baert, Vlady Ravelomanana, Loÿs Thimonier. On the growth of components with non fixed excesses. Discrete Applied Mathematics, 2003, 130 (3), pp.487--493. ⟨10.1016/S0166-218X(03)00326-3⟩. ⟨hal-00153895⟩