## Abstract We shall prove that if __L__ is a 3‐chromatic (so called “forbidden”) graph, and —__R__^__n__^ is a random graph on __n__ vertices, whose edges are chosen independently, with probability __p__, and —__B__^__n__^ is a bipartite subgraph of __R__^__n__^ of maximum size, —__F__^__n__^ is a
Extremal subgraphs for two graphs
✍ Scribed by F.R.K Chung; P Erdös; J Spencer
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 564 KB
- Volume
- 38
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
Let Ex(n, k, µ) denote the maximum number of edges of an n-vertex graph in which every subgraph of k vertices has at most µ edges. Here we summarize some known results of the problem of determining Ex(n, k, µ), give simple proofs, and find some new estimates and extremal graphs. Besides proving new
## Abstract A cubic triangle‐free graph has a bipartite subgraph with at least 4/5 of the original edges. Examples show that this is a best possible result.
The study of graph homomorphisms has a long and distinguished history, with applications in many areas of graph theory. There has been recent interest in counting homomorphisms, and in particular on the question of finding upper bounds for the number of homomorphisms from a graph G into a fixed imag
We determine, to within a constant factor, the maximum size of a digraph that does not contain a topological complete digraph DK p of order p. Let t 1 ( p) be defined for positive p by where D denotes a digraph. We show that 1 16 p 2 < t 1 ( p) ≤ 44 p 2 . We also obtain results for containing topol
We prove that whenever the edge number of a graph of order \(n \geqslant 517\) ensures that it contains every complete graph and every forest with at most \(n\) vertices and at most \(m\) edges, then the graph contains every graph with at most \(n\) vertices and \(m\) edges if \(m<n\). The required