## Abstract A partially ordered set __P__ is called a __kβsphere order__ if one can assign to each element a β __P__ a ball __B__~__a__~ in __R^k^__ so that __a__ < __b__ iff __B__~__a__~ β __B__~__b__~. To a graph __G__ = (__V,E__) associate a poset __P__(__G__) whose elements are the vertices and
A Note on Planar Graphs and Circle Orders
β Scribed by Scheinerman, Edward R.
- Book ID
- 118197518
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 1991
- Tongue
- English
- Weight
- 350 KB
- Volume
- 4
- Category
- Article
- ISSN
- 0895-4801
- DOI
- 10.1137/0404040
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Some new properties of the distribution of elements and vertices with respect to the windows of a connected planar graph G are established. It is also shown that a window matrix of G has properties similar to the properties of an incidence matrix of a graph which is not necessarily planar. A method
A graph G is called (k, d)\*-choosable if, for every list assignment L satisfying [L(v)l = k for all v E V(G), there is an L-coloring of G such that each vertex of G has at most d neighbors colored with the same color as itself. In this note, we prove that every planar graph without 4-cycles and /-c