In thiq paper we prove the following: let G be a graph with k edges, wihich js (k -l)-edgeconnectd, and with all valences 3k k. Let 1 c r~ k be an integer, then (3 -tins a spanning subgraph H, so that all valences in H are ar, with no more than r~/r:] edges. The proof is based on a useful extension
Variations on a theorem of Petersen
β Scribed by K. S. Bagga; L. W. Beineke; G. Chartrand; O. R. Oellermann
- Publisher
- Springer Netherlands
- Year
- 1988
- Tongue
- English
- Weight
- 331 KB
- Volume
- 19
- Category
- Article
- ISSN
- 0031-5303
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π SIMILAR VOLUMES
Goemans, M.X., A generalization of Petersen's theorem, Discrete Mathematics 115 (1993) 277-282. Petersen's theorem asserts that any cubic graph with at most 2 cut edges has a perfect matching. We generalize this classical result by showing that any cubic graph G = (V, E) with at most 1 cut edge has
A famous theorem of Ryser asserts that a v x v zero-one matrix A satisfying AA r --(k -k)I + aJ with k ~ k must satisfy k + (v -1)k = k 2 and ArA (k -k)I + A J; such a matrix A is called the incidence matrix of a symmetric block design. We present a new, e/ementary proof of Ryser's theorem and give