Embeddability of finite distance graphs with a large chromatic number in random graphs
โ Scribed by S. V. Nagaeva
- Book ID
- 111454512
- Publisher
- SP MAIK Nauka/Interperiodica
- Year
- 2008
- Tongue
- English
- Weight
- 177 KB
- Volume
- 77
- Category
- Article
- ISSN
- 1064-5624
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The distance graph G(D) with distance set D={d 1 , d 2 , ...} has the set Z of integers as vertex set, with two vertices i, j ยฅ Z adjacent if and only if |i -j| ยฅ D. We prove that the chromatic number of G(D) is finite whenever inf{d i+1 /d i } > 1 and that every growth speed smaller than this admit
## Abstract An Erratum has been published for this article in Journal of Graph Theory 48: 329โ330, 2005. Let __M__ be a set of positive integers. The distance graph generated by __M__, denoted by __G__(__Z, M__), has the set __Z__ of all integers as the vertex set, and edges __ij__ whenever |__i__
For each pair k, rn of natural numbers there exists a natural number f(k, rn) such that every f ( k , m)-chromatic graph contains a k-connected subgraph of chromatic number at least rn.