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Proof of a Packing Conjecture of Bollobás

Published online by Cambridge University Press:  12 September 2008

János Komlós
Affiliation:
Rutgers University, USAHungarian Academy of Sciences, Hungary
Gábor N. Sárközy
Affiliation:
Rutgers University, USAHungarian Academy of Sciences, Hungary
Endre Szemerédi
Affiliation:
Rutgers University, USAHungarian Academy of Sciences, Hungary

Abstract

Béla Bollobás [1] conjectured the following. For any positive integer Δ and real 0 < c < ½ there exists an n0 with the following properties. If nn0, T is a tree of order n and maximum degree Δ, and G is a graph of order n and maximum degree not exceeding cn, then there is a packing of T and G. Here we prove this conjecture. Auxiliary Theorem 2.1 is of independent interest.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1995

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References

[1]Bollobás, B. (1978) Extremal Graph Theory, Academic Press, London.Google Scholar
[2]Bollobás, B. and Eldridge, S. E. (1978) Packings of graphs and applications to computational complexity. J. Combinatorial Theory (B) 25 105124.CrossRefGoogle Scholar
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[5]Komlós, J. and Sós, V. (1991) Regular subgraphs of graphs. Manuscript.Google Scholar
[6]Lovász, L. (1979) Combinatorial Problems and Exercises. Akadémiai Kiadó, Budapest.Google Scholar
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[8]Szemerédi, E. (1976) Regular partitions of graphs. Colloques Internationaux C.N.R.S. No. 260 – Problèmes Combinatoires et Théorie des Graphes, Orsay, France, pp. 399401.Google Scholar
[9]Szemerédi, E. (1975) On a set containing no k elements in arithmetic progression. Acta Arithmetica XXVII 199245.Google Scholar
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