Results 251 to 260 of about 1,379,637 (289)

Four Pages Are Indeed Necessary for Planar Graphs

Journal of Computational Geometry, 2020
An embedding of a graph in a book consists of a linear order of its vertices along the spine of the book and of an assignment of its edges to the pages of the book, so that no two edges on the same page cross. The book thickness of a graph is the minimum
M. Bekos, M. Kaufmann, Fabian Klute, S. Pupyrev, C. Raftopoulou, T. Ueckerdt   +5 more
semanticscholar   +1 more source

Planar graphs

Graphs and Geometry, 2019
Lawler, Schramm and Werner showed that the scaling limit of the loop-erased random walk on Z2 is SLE2. We consider scaling limits of the loop-erasure of random walks on other planar graphs (graphs embedded into C so that edges do not cross one another ...
Marc Barthelemy
semanticscholar   +1 more source

On Optimal 2- and 3-Planar Graphs

International Symposium on Computational Geometry, 2017
A graph is k-planar if it can be drawn in the plane such that no edge is crossed more than k times. While for k=1, optimal 1-planar graphs, i.e., those with n vertices and exactly 4n-8 edges, have been completely characterized, this has not been the case
M. Bekos, M. Kaufmann, C. Raftopoulou
semanticscholar   +1 more source

Planar Graphs Without 4-Cycles Adjacent to Triangles are DP-4-Colorable

Graphs and Combinatorics, 2017
DP-coloring (also known as correspondence coloring) of a simple graph is a generalization of list coloring. It is known that planar graphs without 4-cycles adjacent to triangles are 4-choosable, and planar graphs without 4-cycles are DP-4-colorable.
Seog-Jin Kim, Xiaowei Yu
semanticscholar   +1 more source

A study on m-polar fuzzy planar graphs

International Journal of Computing Science and Mathematics, 2016
In many practical applications with a graph structure, there may exist crossing between edges which is not allowed in a crisp planar graph. Considering that graphic structures can be used to describe the crossing of edges in an m-polar fuzzy multi-graph ...
G. Ghorai, M. Pal
semanticscholar   +1 more source

Recognizing Optimal 1-Planar Graphs in Linear Time

Algorithmica, 2016
A graph with n vertices is 1-planar if it can be drawn in the plane such that each edge is crossed at most once, and is optimal if it has the maximum of 4n-8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts ...
F. Brandenburg
semanticscholar   +1 more source

Faces and dual of m-polar fuzzy planar graphs

Journal of Intelligent & Fuzzy Systems, 2016
Recently, Ghorai and Pal (12) introduced the notion of m-polar fuzzy planar graphs using the concept of m-polar fuzzy multisets. In this paper, m-polar fuzzy faces and strong m-polar fuzzy faces are defined.
G. Ghorai, M. Pal
semanticscholar   +1 more source

Streaming Algorithms for Estimating the Matching Size in Planar Graphs and Beyond

ACM-SIAM Symposium on Discrete Algorithms, 2015
We consider the problem of estimating the size of a maximum matching when the edges are revealed in a streaming fashion. When the input graph is planar, we present a simple and elegant streaming algorithm that, with high probability, estimates the size ...
Hossein Esfandiari, M. Hajiaghayi, Vahid Liaghat, M. Monemizadeh, Krzysztof Onak   +4 more
semanticscholar   +1 more source

Fuzzy Planar Graphs

IEEE transactions on fuzzy systems, 2015
Fuzzy planar graph is a very important subclass of fuzzy graph. In this paper, two types of edges are mentioned for fuzzy graphs: effective edges and considerable edges.
Sovan Samanta, M. Pal
semanticscholar   +1 more source

The Book Thickness of 1-Planar Graphs is Constant

Algorithmica, 2015
In a book embedding, the vertices of a graph are placed on the “spine” of a book and the edges are assigned to “pages”, so that edges on the same page do not cross.
M. Bekos, Till Bruckdorfer, M. Kaufmann, C. Raftopoulou   +3 more
semanticscholar   +1 more source