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Let S(H) be the minimum degree of the graph H. We prove that a graph H of order n with S(H) ^ (2n —1)/3 contains any graph G of order at most n and maximum degree A(G) < 2 as a subgraph, and this bound is best possible. Furthermore, this result settles the case A(G) = 2 of the well-known conjecture of Bollobas, Catlin and Eldridge on packing two graphs with(More)
Global connectivity and expansion: long cycles and factors in f-connected graphs Abstract Given a function f : N → R, call an n-vertex graph f-connected if separating off k vertices requires the deletion of at least f (k) vertices whenever k ≤ (n − f (k))/2. This is a common generalization of vertex connectivity (when f is constant) and expansion (when f is(More)
In 1972, Erd˝ os and Simonovits [9] asked whether a triangle-free graph with minimum degree greater than n/3, where n is the number of vertices, has chromatic number at most three. Hajnal provided examples of triangle-free graphs with arbitrarily large chromatic number and minimum degree greater than (1/3 − ε)n, for every ε > 0. Häggkvist [10] gave a(More)
Advances in high-throughput genome sequencing demand the development of more efficient ways of examining gene expression at a cellular level. During recent years, polymerase chain reaction (PCR)-based methods have been developed that allow the amplification of mRNA from small amounts of material, even from single animal cells. In parallel, several(More)
In the class of k-connected claw-free graphs, we study the stability of some hamilto-nian properties under a closure operation introduced by the third author. We prove that (i) the properties of pancyclicity, vertex pancyclicity and cycle extendability are not stable for any k (i.e., for any of these properties there is an innnite family of graphs G k of(More)