On the Page Number of Upward Planar Directed ... - Semantic Scholar
On the Page Number of Upward Planar Directed Acyclic Graphs⋆ Fabrizio Frati1,2 , Radoslav Fulek1 , Andres J. Ruiz-Vargas1 1 School of Basic Sciences - École Polytechnique Fédérale de Lausanne, Switzerland {fabrizio.frati,radoslav.fulek,andres.ruizvargas}@epfl.ch 2 Dipartimento di Informatica e Automazione, Università Roma Tre
Abstract. In this paper we study the page number of upward planar directed acyclic graphs. We prove that the page number of any upward planar directed acyclic graph G is a function of the page number of a four-connected subgraph of G; further, we provide an upper bound on the page number of G if G has small diameter; finally, we show that every upward planar directed acyclic graph has small page number if and only if every upward planar directed acyclic graph with small degree does.
1 Introduction A k-page book embedding of a graph G=(V, E) is a total ordering σ of V and a partition of E into subsets E1 , E2 , . . . , Ek , called pages, such that no two edges (u, v) and (w, z) with u
Abstract. In this paper we study the page number of upward planar directed acyclic graphs. We prove that the page number of any upward planar directed acyclic graph G is a function of the page number of a four-connected subgraph of G; further, we provide an upper bound on the page number of G if G has small diameter; finally, we show that every upward planar directed acyclic graph has small page number if and only if every upward planar directed acyclic graph with small degree does.
1 Introduction A k-page book embedding of a graph G=(V, E) is a total ordering σ of V and a partition of E into subsets E1 , E2 , . . . , Ek , called pages, such that no two edges (u, v) and (w, z) with u
