## Abstract An old conjecture of ErdΕs states that there exists an absolute constant __c__ and a set __S__ of density zero such that every graph of average degree at least __c__ contains a cycle of length in __S__. In this paper, we prove this conjecture by showing that every graph of average degre
Unavoidable stars in 3-graphs
β Scribed by F.R.K. Chung
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 403 KB
- Volume
- 35
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let %(n, rn) denote the class of simple graphs on n vertices and rn edges and let G E %(n, rn). There are many results in graph theory giving conditions under which G contains certain types of subgraphs, such as cycles of given lengths, complete graphs, etc. For example, Turan's theorem gives a suff
## Abstract A __parallel minor__ is obtained from a graph by any sequence of edge contractions and parallel edge deletions. We prove that, for any positive integer __k__, every internally 4βconnected graph of sufficiently high order contains a parallel minor isomorphic to a variation of __K__~4,__k