Asymptotic solution of a turán-type problem
✍ Scribed by P. Frankl
- Publisher
- Springer Japan
- Year
- 1990
- Tongue
- English
- Weight
- 214 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0911-0119
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We consider the following analogue of a problem of Turin for interval graphs: Let c = c(n, rn) be the largest integer such that any interval graph with n vertices and at least m edges contains a complete subgraph on c vertices. We determine the value of c(n, m) explicitly.
## Abstract For each __n__ and __k__, we examine bounds on the largest number __m__ so that for any __k__‐coloring of the edges of __K~n~__ there exists a copy of __K~m~__ whose edges receive at most __k−__1 colors. We show that for $k \ge \sqrt{n}\;+\,\Omega(n^{1/3})$, the largest value of __m__ i
Let Tbe a tournament and let c :e(T)--> {1 ..... r} be an r-colouring of the edges of T. The associated reachability graph, denoted by R(T, c) is a directed graph whose vertices are the vertices of T, and a vertex v of R(T, c) dominates a vertex u of R(T, c) iff there is a monochromatic directed pat