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Book Embedding of Graphs on the Projective Plane

SIAM Journal on Discrete Mathematics, 2019
Summary: 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 ...
Kenta Ozeki, Atsuhiro Nakamoto
exaly   +3 more sources

Book Embedding of Toroidal Bipartite Graphs

SIAM Journal on Discrete Mathematics, 2012
Endo 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, Katsuhiro Ota, Kenta Ozeki   +2 more
exaly   +2 more sources