## Abstract A __complete coloring__ of a simple graph __G__ is a proper vertex coloring such that each pair of colors appears together on at least one edge. The __achromatic number__ Ο(__G__) is the greatest number of colors in such a coloring. We say a class of graphs is fragmentable if for any po
Achromatic numbers and graph operations
β Scribed by Pavol Hell; Donald J. Miller
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 510 KB
- Volume
- 108
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
In [5, 61 a criterion for the undecidability of second order theories of classes of graphs is introduced. This criterion leads to a "measure of complexity" of a class of graphs. In this note we introduce some graph theoretical operations and prove that the class of all graphs which have the smallest
It is shown that if G and H are arbitrary fixed graphs and n is sufficiently large, then Also, we prove that r ( K 1 +F, K,) 5 (m+o(l))&(n -+ GO) for any forest Fwhose largest component has m edges. Thus r(Fe, K,) 5 (1 + o(l))&, where Fe = K1 + CK2. We conjecture that r(Fe, K,) -&(n + cm).
## Abstract The ramsey number of any tree of order __m__ and the complete graph of order __n__ is 1 + (__m__ β 1)(__n__ β 1).