Let H be a graph on n vertices and G a collection of n subgraphs of H , one for each vertex. Then G is an orthogonal double cover (ODC) of H if every edge of H occurs in exactly two members of G and any two members share an edge whenever the corresponding vertices are adjacent in H . ODCs of complet
Orthogonal double covers of Kn,n by small graphs
✍ Scribed by Ramadan El-Shanawany; Hans-Dietrich O.F. Gronau; Martin Grüttmüller
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 443 KB
- Volume
- 138
- Category
- Article
- ISSN
- 0166-218X
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✦ Synopsis
An orthogonal double cover (ODC) of Kn is a collection of graphs such that each edge of Kn occurs in exactly two of the graphs and two graphs have precisely one edge in common. ODCs of Kn and their generalizations have been extensively studied by several authors (e.g. in:
📜 SIMILAR VOLUMES
A collection = {GI, CZ, . . . , C,} of spanning subgraphs of K, is called an orthogonal double cover if (i) every edge of K , belongs to exactly two of the Ci's and (ii) any two distinct Ci's intersect in exactly one edge. Chung and West conjectured that there exists an orthogonal double cover of K,
## Seyffarth, K., Hajos' conjecture and small cycle double covers of planar graphs, Discrete Mathematics 101 (1992) 291-306. We prove that every simple even planar graph on n vertices has a partition of its edge set into at most [(n -1)/2] cycles. A previous proof of this result was given by Tao,