The linear arboricity la(G) of a graph G is the minimum number of linear forests that partition the edges of G. Akiyama, Exoo, and Harary conjectured for any simple graph G with maximum degree โ. The conjecture has been proved to be true for graphs having โ =
On line graphs of linear 3-uniform hypergraphs
โ Scribed by Metelsky, Yury; Tyshkevich, Regina
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 154 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
โฆ Synopsis
It is known that the class of line graphs of linear 3-uniform hypergraphs cannot be characterized by a finite list of forbidden induced subgraphs (R. N.
๐ SIMILAR VOLUMES
In this paper all connected line graphs whose second largest eigenvalue does not exceed 1 are characterized. Besides, all minimal line graphs with second largest eigenvalue greater than 1 are determined.
A well-known Tutte's theorem claims that every 3-connected planar graph has a convex embedding into the plane. Tutte's arguments also show that, moreover, for every nonseparating cycle C of a 3-connected graph G, there exists a convex embedding of G such that C is a boundary of the outer face in thi