منابع مشابه
Embedding Spanning Bipartite Graphs of Small Bandwidth
Böttcher, Schacht and Taraz [6] gave a condition on the minimum degree of a graph G on n vertices that ensures G contains every r-chromatic graph H on n vertices of bounded degree and of bandwidth o(n), thereby proving a conjecture of Bollobás and Komlós [15]. We strengthen this result in the case when H is bipartite. Indeed, we give an essentially best-possible condition on the degree sequence...
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Endo [5] proved that every toroidal graph has a book embedding with at most seven pages. In this paper, we prove that every toroidal bipartite graph has a book embedding with at most five pages. In order to do so, we prove that every bipartite torus quadrangulation Q with n vertices admits two disjoint essential simple closed curves cutting the torus into two annuli so that each of the two annu...
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A topological book embedding of a graph is an embedding in a book that carries the vertices in the spine of the book and the edges in the pages so that edges are allowed to cross the spine. Recently, the author has shown that for an arbitrary graph G with n vertices there exists a d + 1page book embedding of G in which each edge crosses the spine logd n times. This paper improves the result for...
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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...
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We find the minimum number k = μ(Σ) for any surface Σ, such that every Σ-embeddable non-bipartite graph is not k-extendable. In particular, we construct the so-called bow-tie graphs C6 ⊲⊳ Pn, and show that they are 3-extendable. This confirms the existence of an infinite number of 3-extendable non-bipartite graphs which can be embedded in the Klein bottle.
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2010
ISSN: 0895-4801,1095-7146
DOI: 10.1137/090765481