منابع مشابه
An obstruction to embedding graphs in surfaces
There is much work done in the theory of embeddings of graphs in closed surfaces. Among the most important results is the solution of the Heawood Map Coloring Problem which includes the determination of the genera of complete graphs. (The reader is referred to the Ringel’s book [8], and also to monographs by White [ 161 and Gross and Tucker [6].) Many nice and powerful techniques were developed...
متن کاملEmbedding graphs in surfaces: MacLane’s theorem for higher genus∗
Given a closed surface S, we characterise the graphs embeddable in S by an algebraic condition asserting the existence of a sparse generating set for their cycle space. When S is the sphere, the condition defaults to MacLane’s planarity criterion.
متن کاملEmbedding grids in surfaces
We show that if a very large grid is embedded in a surface, then a large subgrid is embedded in a disc in the surface. This readily implies that: (a) a minor-minimal graph that does not embed in a given surface has no very large grid; and (b) a minor-minimal k-representative embedding in the surface has no very large grid. Similar arguments show (c) that if G is minimal with respect to crossing...
متن کاملEmbedding Graphs into Embedded Graphs
A drawing of a graph G in the plane is weakly simple if it can be turned into an embedding by an arbitrarily small perturbation. We show that testing, whether a straight-line drawing of a planar graph G in the plane is weakly simple, can be carried out in polynomial time, if a desired embedding of G belongs to a fixed isotopy class. In other words, we show that c-planarity with pipes is tractab...
متن کاملHomogeneously Embedding Stratified Graphs in Stratified Graphs
A 2-stratified graph G is a graph whose vertex set has been partitioned into two subsets, called the strata or color classes of G. Two 2-stratified graphs G and H are isomorphic if there exists a color-preserving isomorphism φ from G to H. A 2-stratified graph G is said to be homogeneously embedded in a 2-stratified graph H if for every vertex x of G and every vertex y of H, where x and y are c...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1984
ISSN: 0095-8956
DOI: 10.1016/0095-8956(84)90014-5