## Abstract A partially ordered set __P__ is called a __k‐sphere order__ if one can assign to each element a ∈ __P__ a ball __B__~__a__~ in __R^k^__ so that __a__ < __b__ iff __B__~__a__~ ⊂ __B__~__b__~. To a graph __G__ = (__V,E__) associate a poset __P__(__G__) whose elements are the vertices and
On ordered graphs and graph orderings
✍ Scribed by Jaroslav Nešetřil
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 290 KB
- Volume
- 51
- Category
- Article
- ISSN
- 0166-218X
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## Abstract We consider graphs __G = (V,E)__ with order ρ = |__V__|, size __e__ = |__E__|, and stability number β~0~. We collect or determine upper and lower bounds on each of these parameters expressed as functions of the two others. We prove that all these bounds are sharp. © __1993 by John Wiley
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