DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory 25(3) (2005) 311-324
DOI: 10.7151/dmgt.1284

TREES WITH -LABELINGS AND DECOMPOSITIONS OF COMPLETE GRAPHS INTO NON-SYMMETRIC ISOMORPHIC SPANNING TREES

Michael Kubesa

Department of Applied Mathematics
Technical University Ostrava
17 listopadu, Ostrava-Poruba 708 33, Czech Republic
e-mail: michael.kubesa.cz

Abstract

We examine constructions of non-symmetric trees with a flexible q-labeling or an α-like labeling, which allow factorization of K2n into spanning trees, arising from the trees with α-labelings.

Keywords: graph decomposition and factorization, graph labeling, α-labeling, flexible q-labeling, α-like labeling.

2000 Mathematics Subject Classification: 05C70, 05C78.

References

[1] P. Eldergill, Decompositions of the complete graph with an even number of vertices (M.Sc. thesis, McMaster University, Hamilton, 1997).
[2] D. Froncek, Cyclic decompositions of complete graphs into spanning trees, Discuss. Math. Graph Theory 24 (2004) 345-352, doi: 10.7151/dmgt.1235.
[3] D. Froncek, Bi-cyclic decompositions of complete graphs into spanning trees, submitted for publication.
[4] D. Froncek and M. Kubesa, Factorizations of complete graphs into spanning trees, Congress. Numer. 154 (2002) 125-134.
[5] A. Rosa, Cyclic decompositions of complete graphs (Ph.D. thesis, Slovak Academy of Science, Bratislava, 1965).
[6] A. Rosa, On certain valuations of the vertices of a graph, in: Theory of Graphs, Intl. Symp. Rome 1966 (Gordon and Breach, Dunod, Paris, 1967) 349-355.
[7] M. Kubesa, Spanning tree factorizations of complete graphs, J. Combin. Math. and Combin. Computing, accepted for publication.

Received 24 February 2004
Revised 11 October 2004