Let G be a bridgeless cubic graph. Fulkerson conjectured that there exist six 1-factors of G such that each edge of G is contained in exactly two of them. Berge conjectured that the edge-set of G can be covered with at most five 1-factors. We prove that the two conjectures are equivalent.
On the berge—sauer conjecture
✍ Scribed by K. R. Parthasarathy; S. Sridharan
- Publisher
- John Wiley and Sons
- Year
- 1982
- Tongue
- English
- Weight
- 115 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
It is proved that a simple 4‐regular graph without K~1,3~ as an induced subgraph has a 3‐regular subgraph.
📜 SIMILAR VOLUMES
## Abstract Berge's elegant dipath partition conjecture from 1982 states that in a dipath partition __P__ of the vertex set of a digraph minimizing , there exists a collection __C__^__k__^ of __k__ disjoint independent sets, where each dipath __P__∈__P__ meets exactly min{|__P__|, __k__} of the ind
## Abstract C. Thomassen proposed a conjecture: Let __G__ be a __k__‐connected graph with the stability number α ≥ __k__, then __G__ has a cycle __C__ containing __k__ independent vertices and all their neighbors. In this paper, we will obtain the following result: Let __G__ be a __k__‐connected gr
## Abstract Gol'dberg has recently constructed an infinite family of 3‐critical graphs of even order. We now prove that if there exists a __p__(≥4)‐critical graph __K__ of odd order such that __K__ has a vertex __u__ of valency 2 and another vertex __v__ ≠ __u__ of valency ≤(__p__ + 2)/2, then ther
If f 1 ðnÞ; . . . ; f r ðnÞ are all prime for infinitely many n; then it is necessary that the polynomials f i are irreducible in Z½X ; have positive leading coefficients, and no prime p divides all values of the product f 1 ðnÞ Á Á Á f r ðnÞ; as n runs over Z: Assuming these necessary conditions, B
## Abstract In [5], Coates and Sinnott formulated a far reaching conjecture linking the values Θ~__F/k,S__~ (1 — __n)__ for even integers __n__ ≥ 2 of an __S__ ‐imprimitive, Galois‐equivariant __L__ ‐function Θ~__F/k,S__~ associated to an abelian extension __F/k__ of totally real number fields to