Geodesic
Orthogonal double covers of complete graphs by fat caterpillars
Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 2, pp. 343-349.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: ODC, orthogonal double cover, graph decomposition, self-orthogonal factorization 
@article{DMGT_2006_26_2_a14,
     author = {Froncek, Dalibor and Leck, Uwe},
     title = {Orthogonal double covers of complete graphs by fat caterpillars},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {343--349},
     publisher = {mathdoc},
     volume = {26},
     number = {2},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2006_26_2_a14/}
}
TY  - JOUR
AU  - Froncek, Dalibor
AU  - Leck, Uwe
TI  - Orthogonal double covers of complete graphs by fat caterpillars
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2006
SP  - 343
EP  - 349
VL  - 26
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2006_26_2_a14/
LA  - en
ID  - DMGT_2006_26_2_a14
ER  - 
%0 Journal Article
%A Froncek, Dalibor
%A Leck, Uwe
%T Orthogonal double covers of complete graphs by fat caterpillars
%J Discussiones Mathematicae. Graph Theory
%D 2006
%P 343-349
%V 26
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2006_26_2_a14/
%G en
%F DMGT_2006_26_2_a14
Froncek, Dalibor; Leck, Uwe. Orthogonal double covers of complete graphs by fat caterpillars. Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 2, pp. 343-349. http://geodesic.mathdoc.fr/item/DMGT_2006_26_2_a14/

[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.

[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.

[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.

[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)5:6433::AID-JCD4>3.0.CO;2-G

[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.