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- S. BRANDT
- 1993

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)

- Stephan Brandt
- 2006

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)

A search has been performed for the Standard Model Higgs boson in the data sample collected with the ALEPH detector at LEP, at centre-of-mass energies up to 209 GeV. An excess of 3 σ beyond the background expectation is found, consistent with the production of the Higgs boson with a mass near 114 GeV/c 2. Much of this excess is seen in the four-jet… (More)

Let G be a graph of order n satisfying d(u) + d(v) ≥ n for every edge uv of G. We show that the circumference—the length of a longest cycle—of G can be expressed in terms of a certain graph parameter, and can be computed in polynomial time. Moreover, we show that G contains cycles of every length between 3 and the circumference, unless G is complete… (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)