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Extremal Graphs for a Graph Packing Theorem of Sauer and Spencer

Published online by Cambridge University Press:  01 May 2007

HEMANSHU KAUL
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA (e-mail: hkaul@math.uiuc.edu, kostochk@math.uiuc.edu)
Corresponding

Abstract

Let G1 and G2 be graphs of order n with maximum degree Δ1 and Δ2, respectively. G1 and G2 are said to pack if there exist injective mappings of the vertex sets into [n], such that the images of the edge sets do not intersect. Sauer and Spencer showed that if , then G1 and G2 pack. We extend this result by showing that if , then G1 and G2 do not pack if and only if one of G1 or G2 is a perfect matching and the other either is with odd or contains .

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Copyright
Copyright © Cambridge University Press 2006

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References

[1]Bollobás, B. (1978) Extremal Graph Theory, Academic Press, London/New York.Google Scholar
[2]Bollobás, B. and Eldridge, S. E. (1978) Packing of graphs and applications to computational complexity. J. Combin. Theory Ser. B 25 105124.CrossRefGoogle Scholar
[3]Catlin, P. A. (1974) Subgraphs of graphs I. Discrete Math. 10 225233.CrossRefGoogle Scholar
[4]Sauer, N. and Spencer, J. (1978) Edge disjoint placement of graphs. J. Combin. Theory Ser. B 25 295302.CrossRefGoogle Scholar
[5]Wozniak, M. (1997) Packing of graphs. Dissertationes Math. 362 78pp.Google Scholar
[6]Yap, H. P. (1988) Packing of graphs: A survey. Discrete Math. 72 395404.CrossRefGoogle Scholar
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