For any 4-regular graph G (possibly with multiple edges), we prove that, if the number N of distinct Euler orientations of G is such that N ≡ 1 (mod 3), then G has a 3-regular subgraph. It gives the new 4-regular graphs with multiple edges which have no 3-regular subgraphs, for which we know the num
Generating all planer graphs regular of degree four
✍ Scribed by Paolo Manca
- Publisher
- John Wiley and Sons
- Year
- 1979
- Tongue
- English
- Weight
- 225 KB
- Volume
- 3
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
All planar connected graphs regular of degree four can be generated from the graph of the octahedron, using four operations.
📜 SIMILAR VOLUMES
## Abstract It has been communicated by P. Manca in this journal that all 4‐regular connected planar graphs can be generated from the graph of the octahedron using simple planar graph operations. We point out an error in the generating procedure and correct it by including an additional operation.
A p-factor of a graph G is a regular spanning subgraph of degree p . For G regular of degree d ( G ) and order 2n, let ( p l , ..., p,) be a partition of d ( G ) , so that p i > 0 ( I S i S r ) and p , i i pr = d(G). If H I . ..., H, are edge-disjoint regular spanning subgraphs of G of degrees p I ,
## Abstract In 1960, Dirac posed the conjecture that __r__‐connected 4‐critical graphs exist for every __r__ ≥ 3. In 1989, Erdős conjectured that for every __r__ ≥ 3 there exist __r__‐regular 4‐critical graphs. In this paper, a technique of constructing __r__‐regular __r__‐connected vertex‐transiti
## Abstract We prove that all 3‐connected 4‐regular planar graphs can be generated from the Octahedron Graph, using three operations. We generated these graphs up to 15 vertices inclusive. Moreover, by including a fourth operation we obtain an alternative to a procedure by Lehel to generate all con