Related papers: Four Pages Are Indeed Necessary for Planar Graphs

An embedding of a graph in a book, called book embedding, consists of a linear ordering of its vertices along the spine of the book and an assignment of its edges to the pages of the book, so that no two edges on the same page cross. The…

In a book embedding of a graph G, the vertices of G are placed in order along a straight-line called spine of the book, and the edges of G are drawn on a set of half-planes, called the pages of the book, such that two edges drawn on a page…

In a book embedding, the vertices of a graph are placed on the spine of a book and the edges are assigned to pages, so that edges on the same page do not cross. In this paper, we prove that every $1$-planar graph (that is, a graph that can…

We show that there are planar graphs that require four pages in any book embedding.

A \emph{book-embedding} of a graph $G$ is an embedding of vertices of $G$ along the spine of a book, and edges of $G$ on the pages so that no two edges on the same page intersect. the minimum number of pages in which a graph can be embedded…

The matching book thickness of a graph is the least number of pages in a book embedding such that each page is a matching. A graph is dispersable if its matching book thickness equals its maximum degree. Minimum page matching book…

A map is a partition of the sphere into regions that are labeled as countries or holes. The vertices of a map graph are the countries of a map. There is an edge if and only if the countries are adjacent and meet in at least one point. For a…

The \emph{matching book embedding} of a graph $G$ is to arrange its vertices on the spine, and draw its edges into the pages so that the edges on every page do not intersect each other and the maximum degree of vertices on every page is…

Every planar graph has a 4-page book embedding and this bound is tight. We show that every 1-planar graph, which is a graph that admits a drawing with at most one crossing per edge, has a 10-page book embedding. In addition, four pages are…

A book embedding of a graph consists of an embedding of its vertices along the spine of a book, and an embedding of its edges on the pages such that edges embedded on the same page do not intersect. The pagenumber is the minimum number of…

The $n$-$book ~embedding$ of a graph $G$ is an embedding of the graph $G$ in an $n$-book with the vertices of $G$ on the spine and each edge to the pages without crossing each other. If the degree of vertices of $G$ at most one in each…

It is shown that the number of pages required for a book embedding of a graph is the maximum of the numbers needed for any of the maximal nonseparable subgraphs and that a plane graph in which every triangle bounds a face has a two-page…

In a dispersable book embedding, the vertices of a given graph $G$ must be ordered along a line l, called spine, and the edges of G must be drawn at different half-planes bounded by l, called pages of the book, such that: (i) no two edges…

The book embedding of a graph $G$ is to place the vertices of $G$ on the spine and draw the edges to the pages so that the edges in the same page do not cross with each other. A book embedding is matching if the vertices in the same page…

We prove that the geometric thickness of graphs whose maximum degree is no more than four is two. All of our algorithms run in O(n) time, where n is the number of vertices in the graph. In our proofs, we present an embedding algorithm for…

A k-page book embedding of a graph G draws the vertices of G on a line and the edges on k half-planes (called pages) bounded by this line, such that no two edges on the same page cross. We study the problem of determining whether G admits a…

The $F$-sum is a new graph operation defined by combining four graph transformation operations with the Cartesian product operation. A matching book embedding of a graph $G$ is a book embedding in which the vertices of $G$ are placed on a…

The $book$ $embedding$ of a graph $G$ is to place the vertices of $G$ on the spine and draw the edges to the pages so that the edges in the same page do not cross with each other. The book embedding is $matching$ if the pages have maximum…

We define the geometric thickness of a graph to be the smallest number of layers such that we can draw the graph in the plane with straight-line edges and assign each edge to a layer so that no two edges on the same layer cross. The…

A $k$-stack layout (also called a $k$-page book embedding) of a graph consists of a total order of the vertices, and a partition of the edges into $k$ sets of non-crossing edges with respect to the vertex order. The stack number (book…