Cyclic decompositions of complete graphs into spanning trees

Dalibor Froncek

Discussiones Mathematicae Graph Theory (2004)

  • Volume: 24, Issue: 2, page 345-353
  • ISSN: 2083-5892

Abstract

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We examine decompositions of complete graphs with an even number of vertices, K 2 n , into n isomorphic spanning trees. While methods of such decompositions into symmetric trees have been known, we develop here a more general method based on a new type of vertex labelling, called flexible q-labelling. This labelling is a generalization of labellings introduced by Rosa and Eldergill.

How to cite

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Dalibor Froncek. "Cyclic decompositions of complete graphs into spanning trees." Discussiones Mathematicae Graph Theory 24.2 (2004): 345-353. <http://eudml.org/doc/270544>.

@article{DaliborFroncek2004,
abstract = {We examine decompositions of complete graphs with an even number of vertices, $K_\{2n\}$, into n isomorphic spanning trees. While methods of such decompositions into symmetric trees have been known, we develop here a more general method based on a new type of vertex labelling, called flexible q-labelling. This labelling is a generalization of labellings introduced by Rosa and Eldergill.},
author = {Dalibor Froncek},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {graph factorization; graph labelling; spanning trees; graph labeling},
language = {eng},
number = {2},
pages = {345-353},
title = {Cyclic decompositions of complete graphs into spanning trees},
url = {http://eudml.org/doc/270544},
volume = {24},
year = {2004},
}

TY - JOUR
AU - Dalibor Froncek
TI - Cyclic decompositions of complete graphs into spanning trees
JO - Discussiones Mathematicae Graph Theory
PY - 2004
VL - 24
IS - 2
SP - 345
EP - 353
AB - We examine decompositions of complete graphs with an even number of vertices, $K_{2n}$, into n isomorphic spanning trees. While methods of such decompositions into symmetric trees have been known, we develop here a more general method based on a new type of vertex labelling, called flexible q-labelling. This labelling is a generalization of labellings introduced by Rosa and Eldergill.
LA - eng
KW - graph factorization; graph labelling; spanning trees; graph labeling
UR - http://eudml.org/doc/270544
ER -

References

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  1. [1] J. Bosák, Decompositions of Graphs (Kluwer, Dordrecht, 1990). Zbl0701.05042
  2. [2] P. Eldergill, Decompositions of the complete graph with an even number of vertices (M.Sc. thesis, McMaster University Hamilton, 1997). 
  3. [3] D. Froncek and M. Kubesa, Factorizations of complete graphs into spanning trees, Congressus Numerantium 154 (2002) 125-134. Zbl1021.05083
  4. [4] J.A. Gallian, A dynamic survey of graph labeling, Electronic Journal of Combinatorics DS6 (2001). Zbl0953.05067
  5. [5] G. Ringel, Problem 25, in: Theory of Graphs and its Applications, (Proc. Symp. Smolenice 1963) ed., M. Fiedler (Academia, Prague, 1964) 162. 
  6. [6] A. Rosa, Cyclic decompositions of complete graphs (Ph.D. thesis, Slovak Academy of Science, Bratislava, 1965). 
  7. [7] A. Rosa, On certain valuations of the vertices of a graph, Theory of Graphs (Intl. Symp. Rome 1966), Gordon and Breach, Dunod, Paris (1967) 349-355. 

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