Book-Embeddings in Graphs

• Main Authors: I-Fan Sun, 孫一凡
• Other Authors: Hung-Lin Fu
• Format: Others
• Language: en_US
• Published: 2001
• Online Access: http://ndltd.ncl.edu.tw/handle/79326643514959070733

博士 === 國立交通大學 === 應用數學系 === 89 === A book is a set of half-planes (the pages of the book) that share a common boundary line (the spine of the book). An embedding of a simple undirected graph of G (a pair of vertices are connected by at most one edge) in a book consists of an ordering of the vertices of G along the spine (horizontal line) of the book, together with an assignment of each edge of G to a page of the book, in which edges assigned to the same page do not cross. The minimum number of pages in which a graph G can be embedded is its pagenumber, p(G). And the width of a page is the maximum number of edges that cross any line perpendicular to the spine of the book. The width of a book embedding, w(G), is the maximum width of any page of the book. In devising an embedding, One strives to minimize both the number of pages used, the maximum width of any page and the number of different types. In this thesis, the main results in Chapter 2 focus on the pagenumber and the pagewidth of trees, X-trees, complete graphs and the k-depth Kn-cylinder C(k,n). Then, in Chapter 3 we study the typenumber of lattice graphs and trees.