@article{banukumar2013,
author = {Banukumar, Mahavir},
title = {An Embedding Algorithm for a Specialcase of Extended Grids},
year = {2013},
month = {3},
volume = {5},
pages = {40--45},
journal = {The Bulletin of Society for Mathematical Services and Standards},
doi = {10.18052/www.scipress.com/BSMaSS.5.40},
keywords = {Book Embedding, Book Thickness, Page Number, VLSI Design},
abstract = {A book consists of a line in the 3-dimensional space, called the spine, and a number of pages, each a half-plane with the spine as boundary. A book embedding ($\pi$,$\rho$) of a graph consists of a linear ordering of $\pi$, of vertices, called the spine ordering, along the spine of a book and an assignment $\rho$, of edges to pages so that edges assigned to the same page can be drawn on that page without crossing. That is, we cannot find vertices u, v, x, y with $\pi$(u) < $\pi$(x) < $\pi$(v) < $\pi$(y), yet the edges uv and xy are assigned to the same page, that is $\rho$(uv) = $\rho$(xy). The book thickness or page number of a graph G is the minimum number of pages in required to embed G in a book. In this paper we consider the extended grid and prove that the 1xn extended grid can be embedded in two pages. We also give a linear time algorithm to embed the 1xn extended grid in two pages.}
}