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Connectedness of the Degree Bounded Star Process

Published online by Cambridge University Press:  20 May 2003

CATHERINE GREENHILL ,
ANDRZEJ RUCIŃSKI  and
NICHOLAS C. WORMALD
CATHERINE GREENHILL
Affiliation:
Department of Mathematics and Statistics, University of Melbourne VIC 3010, Australia (e-mail: csg@ms.unimelb.edu.au)
ANDRZEJ RUCIŃSKI
Affiliation:
Department of Discrete Mathematics, Adam Mickiewicz University, Poznań, Poland (e-mail: rucinski@amu.edu.pl)
NICHOLAS C. WORMALD
Affiliation:
Department of Mathematics and Statistics, University of Melbourne VIC 3010, Australia (e-mail: nick@ms.unimelb.edu.au)
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Abstract

In this paper we consider a random star $d$-process which begins with $n$ isolated vertices, and in each step chooses randomly a vertex of current minimum degree $\delta$, and connects it with $d - \delta$ random vertices of degree less than $d$. We show that, for $d \geqslant 3$, the resulting final graph is connected with probability $1 - o(1)$, and moreover that, for suficiently large $d$, it is $d$-connected with probability $1 - o(1)$.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 12 , Issue 3 , May 2003 , pp. 269 - 283
Copyright
© 2003 Cambridge University Press

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