𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Variations on a theorem of Petersen

✍ 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

No coin nor oath required. For personal study only.


πŸ“œ SIMILAR VOLUMES


On Petersen's graph theorem
✍ Nathan Linial πŸ“‚ Article πŸ“… 1981 πŸ› Elsevier Science 🌐 English βš– 399 KB

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

A generalization of Petersen's theorem
✍ Michel X. Goemans πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 338 KB

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

Variations on a theorem of Ryser
✍ Dasong Cao; V. ChvΓ‘tal; A.J. Hoffman; A. Vince πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 304 KB

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