# Orthogonal double covers of complete graphs by fat caterpillars

Discussiones Mathematicae Graph Theory (2006)

- Volume: 26, Issue: 2, page 343-349
- ISSN: 2083-5892

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topDalibor Froncek, and Uwe Leck. "Orthogonal double covers of complete graphs by fat caterpillars." Discussiones Mathematicae Graph Theory 26.2 (2006): 343-349. <http://eudml.org/doc/270256>.

@article{DaliborFroncek2006,

abstract = {An orthogonal double cover (ODC) of the complete graph Kₙ by some graph G is a collection of n spanning subgraphs of Kₙ, all isomorphic to G, such that any two of the subgraphs share exactly one edge and every edge of Kₙ is contained in exactly two of the subgraphs. A necessary condition for such an ODC to exist is that G has exactly n-1 edges. We show that for any given positive integer d, almost all caterpillars of diameter d admit an ODC of the corresponding complete graph.},

author = {Dalibor Froncek, Uwe Leck},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {ODC; orthogonal double cover; graph decomposition; self-orthogonal factorization},

language = {eng},

number = {2},

pages = {343-349},

title = {Orthogonal double covers of complete graphs by fat caterpillars},

url = {http://eudml.org/doc/270256},

volume = {26},

year = {2006},

}

TY - JOUR

AU - Dalibor Froncek

AU - Uwe Leck

TI - Orthogonal double covers of complete graphs by fat caterpillars

JO - Discussiones Mathematicae Graph Theory

PY - 2006

VL - 26

IS - 2

SP - 343

EP - 349

AB - An orthogonal double cover (ODC) of the complete graph Kₙ by some graph G is a collection of n spanning subgraphs of Kₙ, all isomorphic to G, such that any two of the subgraphs share exactly one edge and every edge of Kₙ is contained in exactly two of the subgraphs. A necessary condition for such an ODC to exist is that G has exactly n-1 edges. We show that for any given positive integer d, almost all caterpillars of diameter d admit an ODC of the corresponding complete graph.

LA - eng

KW - ODC; orthogonal double cover; graph decomposition; self-orthogonal factorization

UR - http://eudml.org/doc/270256

ER -

## References

top- [1] H.-D.O.F. Gronau, M. Grüttmüller, S. Hartmann, U. Leck and V. Leck, On orthogonal double covers of graphs, Des. Codes Cryptogr. 27 (2002) 49-91, doi: 10.1023/A:1016546402248. Zbl1001.05091
- [2] H.-D.O.F. Gronau, R.C. Mullin and A. Rosa, Orthogonal double covers of complete graphs by trees, Graphs Combin. 13 (1997) 251-262. Zbl0885.05093
- [3] U. Leck, A class of 2-colorable orthogonal double covers of complete graphs by hamiltonian paths, Graphs Combin. 18 (2002) 155-167, doi: 10.1007/s003730200010. Zbl0988.05074
- [4] U. Leck and V. Leck, On orthogonal double covers by trees, J. Combin. Des. 5 (1997) 433-441, doi: 10.1002/(SICI)1520-6610(1997)5:6<433::AID-JCD4>3.0.CO;2-G Zbl0914.05014
- [5] U. Leck and V. Leck, Orthogonal double covers of complete graphs by trees of small diameter, Discrete Appl. Math. 95 (1999) 377-388, doi: 10.1016/S0166-218X(99)00087-6. Zbl0932.05075

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