## Abstract A graph __G__ is a quasi‐line graph if for every vertex __v__ ∈ __V__(__G__), the set of neighbors of __v__ in __G__ can be expressed as the union of two cliques. The class of quasi‐line graphs is a proper superset of the class of line graphs. Hadwiger's conjecture states that if a grap
Hadwiger's Conjecture is True for Almost Every Graph
✍ Scribed by Bollobás, B.; Catlin, P.A.; Erdös, P.
- Book ID
- 123401836
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 332 KB
- Volume
- 1
- Category
- Article
- ISSN
- 0195-6698
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📜 SIMILAR VOLUMES
## Abstract Hadwiger's conjecture states that every graph with chromatic number χ has a clique minor of size χ. In this paper we prove a weakened version of this conjecture for the class of claw‐free graphs (graphs that do not have a vertex with three pairwise nonadjacent neighbors). Our main resul
An L(2, 1)-labeling of a graph G is defined as a function f from the vertex set V (G) into the nonnegative integers such that for any two vertices x, y, |f Griggs and Yeh conjectured that λ 2,1 (G) ≤ ∆ 2 for any simple graph with maximum degree ∆ ≥ 2. In this paper, we consider the total graph T (G