Orthogonal double covers of complete graphs by fat caterpillars

• Autorzy: Dalibor Froncek , Uwe Leck
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 05C70: Factorization, matching, partitioning, covering and packing
• 05B40: Packing and covering

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2006
• Tom: 26
• Numer: 2
• Strony: 343-349

Daty

wydano

2006

Twórcy

autor

Dalibor Froncek

• Department of Mathematics and Statistics, University of Minnesota Duluth, 1117 University Dr, Duluth, MN 55812, USA

autor

Uwe Leck

• Institut für Mathematik, Universität Rostock, 18051 Rostock, Germany

Bibliografia

• [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)5:6<433::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.

Identyfikatory

DOI

10.7151/dmgt.1325