Book embedding of 3-crossing-critical graphs with rational average degree between 3.5 and 4
Benny Pinontoan, Jullia Titaley, Chriestie E.J.C. Montolalu · IOP Conference Series Materials Science and Engineering · 2019
Abstract We consider the graphs P(m, n) with average degree between 3.5 and 4, made up of m identical pieces together with n identical pieces glued together in a circular fashion, such that in any drawing of P(m, n) on the plane, there are exactly three pairwise edges crossings, and when deleting any edge of the graph, the number of crossings of the remaining graph decreases. We then embed P(m, n) into a book such that the vertices are put on a line called the spine and the edges are put on half-planes called the pages, which have the spine as their common boundary, without crossings. In this paper, we show that the minimal number of pages needed to embed P(m, n) into a book is three.