A paopm graph G has no isolated points. I t s R m e y r u m b a r ( G ) i s the m i n i m p such that every 2-coloring of the edges of K contains a monochromatic G. The Ramhey m & t @ m y R(G) i s P the r (G) ' With j u s t one exception, namely Kq, we determine R(G) f o r proper graphs u i t h a t
A Ramsey property for graph invariants
β Scribed by Fred Buckley
- Publisher
- John Wiley and Sons
- Year
- 1980
- Tongue
- English
- Weight
- 235 KB
- Volume
- 4
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
We consider the problem of which graph invariants have a certain property relating to Ramsey's theorem. Invariants which have this property are called Ramsey functions. We examine properties of chains of graphs associated with Ramsey functions. Methods are developed which enable one to prove that a given invariant is not a Ramsey function. Results for several familiar invariants are presented.
π SIMILAR VOLUMES
For a graph F and natural numbers a 1 ; . . . ; a r ; let F ! Γ°a 1 ; . . . ; a r Γ denote the property that for each coloring of the edges of F with r colors, there exists i such that some copy of the complete graph K ai is colored with the ith color. Furthermore, we write Γ°a 1 ; . . . ; a r Γ ! Γ°b
## Abstract The correlation between molecular path numbers and chemical shift sums found previously in smaller alkanes is extended to larger alkanes. Using data on alkanes with 2β31 carbon atoms a satisfactory regression equation (__R__ = 0.999 and __S__ = 7.5 is derived based on a single molecular