## Abstract Usually __dimension__ should be an integer valued parameter. We introduce a refined version of dimension for graphs, which can assume a value [__t__โโโ1 โ __t__], thought to be between __t__โโโ1 and __t__. We have the following two results: (a) a graph is outerplanar if and only if its
Planarity and Edge Poset Dimension
โ Scribed by Hubert de Fraysseix; Patrice Ossona de Mendez
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 291 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Given a finite graded poset with labeled Hasse diagram, we construct a quasisymmetric generating function for chains whose labels have fixed descents. This is a common generalization of a generating function for the flag f-vector defined by Ehrenborg and of a symmetric function associated with certa
It is proved that any edge of a Pconnected non-planar graph G of order a t least 6 lies in a subdivision of K3,3 in G. For any 3-connected non-planar graph G of order a t least 6 we show that G contains at most four edges which belong to no subdivisions of K3,3 in G.
An edge or face of an embedded graph is light if the sum of the degrees of the vertices incident with it is small. This paper parallelizes four inequalities on the number of light edges and light triangles from the plane to the projective plane. Each of the four inequalities is shown to be the best
Let G be a planar graph and let g(G) and ร(G) be its girth and maximum degree, respectively. We show that G has an edge-partition into a forest and a subgraph H so that (i) -cycles (though it may contain 3-cycles). These results are applied to find the following upper bounds for the game coloring n