Titlebook: ;

Phenothiazines

分散

inconceivable

Bitonic ,-orderings of Biconnected Planar Graphsy that is required by many drawing methods. In this paper, we propose a new type of .-ordering for biconnected planar graphs that relates the ordering to the embedding. We describe a linear-time algorithm to obtain such an ordering and demonstrate its capabilities with two applications.

probate

強(qiáng)化

Fan-Planar Graphs: Combinatorial Properties and Complexity Resultsho proved that every .-vertex fan-planar drawing has at most 5.???10 edges, and that this bound is tight for .?≥?20. We extend their result from both the combinatorial and the algorithmic point of view. We prove tight bounds on the density of constrained versions of fan-planar drawings and study the

描述

On the Recognition of Fan-Planar and Maximal Outer-Fan-Planar Graphssed more than once, is crossed by a bundle of two or more edges incident to a common vertex. A graph is . if it has a fan-planar embedding in which every vertex is on the outer face. If, in addition, the insertion of an edge destroys its outer-fan-planarity, then it is ...In this paper, we present a

Mitigate

Agronomy

A Crossing Lemma for the Pair-Crossing Numbernown that there is a constant .?≥?1/64 such that for every (not too sparse) graph . with . vertices and . edges .. This bound is tight, up to the constant .. Here we show that .?≥?1/34.2 if . is drawn without adjacent crossings.

精致

biopsy

Erratum to: A New Focusing AID,where Γ. and Γ. are required to be . (i.e., they can have crossings provided that there are no three mutually crossing edges). This relaxation allows for the simultaneous embedding of pairs of planar graphs that are not simultaneously embeddable in the classical SGE setting and opens up to several new interesting research questions.