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Book Embedding of Graphs on the Projective Plane
SIAM Journal on Discrete Mathematics, 2019Summary: For a positive integer \(k\), a book (with \(k\) pages) is a topological space consisting of a spine, which is a line, and \(k\) pages, which are half-planes with the spine as their boundary. We say that a graph \(G\) admits a \(k\)-page book embedding or is \(k\)-page book embeddable if there exists a linear ordering of the vertices on the ...
Atsuhiro Nakamoto, Kenta Ozeki
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Embedding Outerplanar Graphs in Small Books
SIAM Journal on Algebraic and Discrete Methods, 1987A book consists of a number of half-planes (pages) sharing a common boundary line (the spine). A book embedding of a graph embeds the vertices on the spine and each edge in some page so that each page contains a plane subgraph. The width of a page is the maximum number of edges that intersect any half-line perpendicular to the spine in the page.
Lenwood Heath
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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 +2 more
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Topological Book Embedding of Bipartite Graphs [PDF]
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2006 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+1-page book embedding of G in which each edge crosses the spine logdn ...
Miki Miyauchi
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The book embedding of ordered sets [PDF]
, 2013 A large number of important problems in different areas can be expressed as graph layout problems whose objective is to determine a linear layout in such way that a certain objective cost is optimized. In a book embedding for an ordered set, the elements are embedded on the spine of the book to form a linear extension.
Alhashem, Mustafa
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