The concept of subcontraction-equivalence is defined, and 14 graphtheoretic properties are exhibited that are all subcontraction-equivalent if Hadwiger's conjecture is true. Some subsets of these properties are proved to be subcontraction-equivalent anyway. Hadwiger's conjecture is expressed as the
A case of hadwiger's conjecture
β Scribed by Michael O. Albertson
- Publisher
- Elsevier Science
- Year
- 1973
- Tongue
- English
- Weight
- 127 KB
- Volume
- 4
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
In this paper, we are concerned with vertex colorings, i.e., assignments of integers to the vertices of a graph.
We recall Hadwiger's Conjecture.
Hadwiger's Conjecture. If G is a graph with chromatic number r then G is contractible to K r.
Hadwiger's Conjecture is known to be true for r less than five. In the case of r = 5, it is equivalent to the Four Color Conjecture.
π SIMILAR VOLUMES
## Abstract A graph __G__ is a quasiβline graph if for every vertex __v__ β __V__(__G__), the set of neighbors of __v__ in __G__ can be expressed as the union of two cliques. The class of quasiβline graphs is a proper superset of the class of line graphs. Hadwiger's conjecture states that if a grap
## Abstract A Short proof is given of the theorem that every grph that does not have __K__~4~ as a subcontraction is properly vertex 3βcolorable.