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Topological Book Embedding of Bipartite Graphs
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2006A 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+1-page book embedding of G in which each edge crosses the spine logdn ...
M. Miyauchi
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Book Embedding of Toroidal Bipartite Graphs
SIAM Journal on Discrete Mathematics, 2012Endo 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 noncontractible simple closed curves cutting the torus
Atsuhiro Nakamoto, K. Ota, K. Ozeki
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Embedding the mesh in books [PDF]
PACRIM. 2005 IEEE Pacific Rim Conference on Communications, Computers and signal Processing, 2005., 2005 In this paper, we study the linear layout problem of the rectangular mesh by the embedding-in-book technique. Embedding a graph in a book is to place nodes on the spine of a book and to draw the edges such that edges residing in a page do not cross. We propose a scheme to embed an h /spl times/ w rectangular mesh with two pages and book width Min(h,w ...
Ka-Lok Ng +4 more
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Degree constrained book embeddings [PDF]
Journal of Algorithms, 2002 Summary: A book embedding of a graph consists of a linear ordering of the vertices along a line in 3-space (the spine) and an assignment of edges to half-planes with the spine as boundary (the pages) so that edges assigned to the same page can be drawn on that page without crossings.
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Embedding generalized Petersen graph in books
Chinese Annals of Mathematics, Series B, 2016A book embedding of a graph G consists of placing the vertices of G on a spine and assigning edges of the graph to pages so that edges in the same page do not cross each other. The page number is a measure of the quality of a book embedding which is the minimum number of pages in which the graph G can be embedded. In this paper, the authors discuss the
Bin Zhao +3 more
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Upward Topological Book Embeddings of DAGs [PDF]
SIAM Journal on Discrete Mathematics, 2011 Let G be a directed acyclic graph (DAG). An upward (k,h)-topological book embedding of G is an upward book embedding on k pages of a subdivision of G where every edge is replaced by a path having at most h+2 vertices. In this paper it is proved that every DAG with n vertices admits an upward (d+1, 2⌈logdn⌉-1)-topological book embedding, where d is any ...
DI GIACOMO, Emilio +2 more
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Book Embeddings of Regular Graphs
SIAM Journal on Discrete Mathematics, 2015In the influential paper in which he proved that every graph with $m$ edges can be embedded in a book with $O({m}^{1/2})$ pages, Malitz proved the existence of $d$-regular $n$-vertex graphs that require $\Omega(\sqrt{d}n^{\frac{1}{2}-\frac{1}{d}})$ pages. In view of the $O({m}^{1/2})$ bound, this last bound is tight when $d > \log{n}$, and Malitz asked
Gelasio Salazar, József Balogh
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Embedding the incomplete hypercube in books
Information Processing Letters, 2005In this paper, we study the linear layout problem of an incomplete hypercube by the embedding-in-book technique. An incomplete hypercube is a generalization of the hypercube in the sense that the number of nodes can be an arbitrary number. Embedding a graph in a book is to place nodes on the spine of a book and to draw the edges such that edges ...
Jywe-Fei Fang, Kuan-Chou Lai
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Embedding Model Design for Producing Book Recommendation
International Conference on Information Management and Technology, 2019Internet services often recommend contents to users in order to maintain the interaction. Recommendation system plays a major role to formulate and produce a series of recommendation based on users’ behavior. Surprisingly, user-generated scoring or known
R. Rahutomo +3 more
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