Dirac proved in 1952 that every 2-connected graph of order n and minimum degree k admits a cycle of length at least minfn; 2kg: As a possible improvement, Woodall conjectured in 1975 that if a 2-connected graph of order n has at least n 2 ΓΎ k vertices of degree at least k; then it has a cycle of len
A Remark on a Graph-Covering Conjecture of D. R. Woodall
β Scribed by Zelinka, B.
- Book ID
- 120097741
- Publisher
- Oxford University Press
- Year
- 1973
- Tongue
- English
- Weight
- 46 KB
- Volume
- s2-6
- Category
- Article
- ISSN
- 0024-6107
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## Abstract In 1978 Woodall [6] conjectured the following: in a planar digraph the size of a shortest cycle is equal to the maximum cardinality of a collection of disjoint tranversals of cycles. We prove that this conjecture is true when the digraph is seriesβparallel. In fact, we prove a stronger
Let F be a connected graph. F is said to be interval-regular if I F~\_ l(u) uF(x )J =. i holds for all vertices u and x ~ Fi(u), i > 0. For u, v e F, let I (u, v) denote the set of all vertices on a shortest path connecting u, v. A subset W of V(F) is said to be convex if l(u,v) c W holds for each u