Colored Point-set Embeddings of Acyclic Graphs

08/30/2017
by   Emilio Di Giacomo, et al.
0

We show that any planar drawing of a forest of three stars whose vertices are constrained to be at fixed vertex locations may require Ω(n^2/3) edges each having Ω(n^1/3) bends in the worst case. The lower bound holds even when the function that maps vertices to points is not a bijection but it is defined by a 3-coloring. In contrast, a constant number of bends per edge can be obtained for 3-colored paths and for 3-colored caterpillars whose leaves all have the same color. Such results answer to a long standing open problem.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
01/31/2022

Max Flow Vitality of Edges and Vertices in Undirected Planar Graphs

We study the problem of computing the vitality with respect to max flow ...
research
08/30/2021

Simplifying Non-Simple Fan-Planar Drawings

A drawing of a graph is fan-planar if the edges intersecting a common ed...
research
01/17/2021

Simultaneous Embedding of Colored Graphs

A set of colored graphs are compatible, if for every color i, the number...
research
11/15/2018

A Note On Universal Point Sets for Planar Graphs

We investigate which planar point sets allow simultaneous straight-line ...
research
11/04/2020

Max-flow vitality in undirected unweighted planar graphs

We show a fast algorithm for determining the set of relevant edges in a ...
research
01/15/2018

Searching for Maximum Out-Degree Vertices in Tournaments

A vertex x in a tournament T is called a king if for every vertex y of T...
research
10/01/2021

Spirality and Rectilinear Planarity Testing of Independent-Parallel SP-Graphs

We study the long-standing open problem of efficiently testing rectiline...

Please sign up or login with your details

Forgot password? Click here to reset