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Matchings in Lattice Graphs and Hamming Graphs

Published online by Cambridge University Press:  12 September 2008

Martin Aigner  and
Regina Klimmek
Martin Aigner
Affiliation:
II. Mathematisches Institut, Freie Universität Berlin, Arnimallee 3, D-14195 Berlin, Germany
Regina Klimmek
Affiliation:
II. Mathematisches Institut, Freie Universität Berlin, Arnimallee 3, D-14195 Berlin, Germany
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Abstract

In this paper we solve the following problem on the lattice graph L(m1,…,mn) and the Hamming graph H(m1,…,mn), generalizing a result of Felzenbaum-Holzman-Kleitman on the n-dimensional cube (all mi = 2): Characterize the vectors (s1.…,sn) such that there exists a maximum matching in L, respectively, H with exactly si edges in the ith direction.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 3 , Issue 2 , June 1994 , pp. 157 - 166
Copyright
Copyright © Cambridge University Press 1994

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References

[1]Felzenbaum, A., Holzman, R. and Kleitman, D. J. (1993) Packing lines in a hypercube. Discrete Math. 117, 107–112.CrossRefGoogle Scholar
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[3]Montroll, E. (1964) Lattice Statistics. In: Beckenbach, (ed.) Applied Combinatorial Mathematics, Wiley.Google Scholar
[4]Proceedings of conference in honour of Prof. Erd⋯os’ 80th birthday,Cambridge University Press (1994).Google Scholar