Titlebook: ;

公司

沉思的鱼

Minimizing an Uncrossed Collection of Drawings satisfy some property that is useful for graph visualization. We propose investigating a property where each edge is not crossed in at least one drawing in the collection. We call such collection .. This property is motivated by a quintessential problem of the crossing number, where one asks for a

敬礼

Dissonance

放肆的我

On 3-Coloring Circle Graphsnd only if their endpoints are pairwise distinct and alternate in .. Therefore, the problem of determining whether . has a .-page book embedding with spine order . is equivalent to deciding whether . can be colored with . colors. Finding a .-coloring for a circle graph is known to be NP-complete for

insurgent

The Complexity of Recognizing Geometric Hypergraphsf a hypergraph ., each vertex . is associated with a point . and each hyperedge . is associated with a connected set . such that . for all .. We say that a given hypergraph . is . by some (infinite) family . of sets in ., if there exist . and . such that (., .) is a geometric representation of .. Fo

心胸狭窄

On the Complexity of Lombardi Graph Drawingertices have perfect angular resolution, i.e., all angles incident to a vertex . have size .. We prove that it is .-complete to determine whether a given graph admits a Lombardi drawing respecting a fixed cyclic ordering of the incident edges around each vertex. In particular, this implies .-hardnes

surmount

VEST

https://doi.org/10.1007/978-1-349-15038-0We study two notions of fan-planarity introduced by (Cheong et al., GD22), called weak and strong fan-planarity, which separate two non-equivalent definitions of fan-planarity in the literature. We prove that not every weakly fan-planar graph is strongly fan-planar, while the upper bound on the edge density is the same for both families.

TRAWL

Weakly and Strongly Fan-Planar GraphsWe study two notions of fan-planarity introduced by (Cheong et al., GD22), called weak and strong fan-planarity, which separate two non-equivalent definitions of fan-planarity in the literature. We prove that not every weakly fan-planar graph is strongly fan-planar, while the upper bound on the edge density is the same for both families.