On minimum matrix representation of closure operations
Discrete Applied Mathematics
Two conjectures of Demetrovics, Furedi, and Katona, concerning partitions
Discrete Mathematics
Self-orthogonal Hamilton path decompositions
Discrete Mathematics - Special volume: Designs and Graphs
On Orthogonal Double Covers of Graphs
Designs, Codes and Cryptography
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
Minimum matrix representation of closure operations
Discrete Applied Mathematics
Orthogonal double covers of general graphs
Discrete Applied Mathematics
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An orthogonal double cover (ODC) of K"n is a collection of graphs such that each edge of K"n occurs in exactly two of the graphs and two graphs have precisely one edge in common. ODCs of K"n and their generalizations have been extensively studied by several authors (e.g. in: J.H. Dinitz, D.R. Stinson (Eds.), Contemporary Design Theory, Wiley, New York, 1992, pp. 13-40 (Chapter 2); Design Codes Cryptography 27 (2002) 49; Graphs Combin. 13 (1997) 251; V. Leck, Orthogonal double covers of K"m, Ph.D. Thesis, Universitat Rostock, 2000). In this paper, we investigate ODCs where the graph to be covered twice is K"n","n and all graphs in the collection are isomorphic to a given small graph G. We prove that there exists an ODC of K"n","n by all proper subgraphs G of K"n","n for 1=