DeepAI AI Chat
Log In Sign Up

Convexity-Increasing Morphs of Planar Graphs

02/19/2018
by   Linda Kleist, et al.
0

We study the problem of convexifying drawings of planar graphs. Given any planar straight-line drawing of a 3-connected graph, we show how to morph the drawing to one with convex faces while maintaining planarity at all times. Furthermore, the morph is convexity increasing, meaning that angles of inner faces never change from convex to reflex. We give a polynomial time algorithm that constructs such a morph as a composition of a linear number of steps where each step either moves vertices along horizontal lines or moves vertices along vertical lines.

READ FULL TEXT

page 1

page 2

page 3

page 4

03/12/2019

Cubic Planar Graphs that cannot be Drawn on few Lines

For every integer ℓ, we construct a cubic 3-vertex-connected planar bipa...
08/21/2018

Monotone Drawings of k-Inner Planar Graphs

A k-inner planar graph is a planar graph that has a plane drawing with a...
03/11/2021

Upward Planar Drawings with Three and More Slopes

We study upward planar straight-line drawings that use only a constant n...
01/13/2023

Primal-Dual Cops and Robber

Cops and Robber is a family of two-player games played on graphs in whic...
03/18/2021

A graph theoretical approach to the firebreak locating problem

In the last decade, wildfires have become wider and more destructive. Th...
02/15/2022

Generalizing continuous flexible Kokotsakis belts of the isogonal type

Kokotsakis studied the following problem in 1932: Given is a rigid close...
05/30/2023

A Schnyder-type drawing algorithm for 5-connected triangulations

We define some Schnyder-type combinatorial structures on a class of plan...