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Asymptotic Solutions of nonlinear difference equations

I. P. van den Berg — 2008

Annales de la faculté des sciences de Toulouse Mathématiques

We study the asymptotics of first-order nonlinear difference equations. In particular we present an asymptotic functional equation for potential asymptotic behaviour, and a theorem stating sufficient conditions for the existence of an actual solution with such asymptotic behaviour.

Minimal claw-free graphs

P. Dankelmann;  Henda C. Swart;  P. van den Berg;  Wayne Goddard;  M. D. Plummer — 2008

Czechoslovak Mathematical Journal

A graph G is a minimal claw-free graph (m.c.f. graph) if it contains no K 1 , 3 (claw) as an induced subgraph and if, for each edge e of G , G - e contains an induced claw. We investigate properties of m.c.f. graphs, establish sharp bounds on their orders and the degrees of their vertices, and characterize graphs which have m.c.f. line graphs.

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