scholarly journals Finding small simple cycle separators for 2-connected planar graphs

1986 ◽  
Vol 32 (3) ◽  
pp. 265-279 ◽  
Author(s):  
Gary L. Miller
Keyword(s):  
Planar Graphs ◽  
Simple Cycle

Short and Simple Cycle Separators in Planar Graphs

2013 ◽  
pp. 26-40 ◽  
Author(s):  
Eli Fox-Epstein ◽  
Shay Mozes ◽  
Phitchaya Mangpo Phothilimthana ◽  
Christian Sommer
Keyword(s):  
Planar Graphs ◽  
Simple Cycle

scholarly journals Geometric Presentations of Braid Groups for Particles on a Graph

2021 ◽  
Author(s):  
Byung Hee An ◽  
Tomasz Maciazek
Keyword(s):  
Braid Group ◽  
Planar Graphs ◽  
Braid Groups ◽  
Quantum Statistics ◽  
Simple Cycle ◽  
Full Description ◽  
Baxter Equation ◽  
Connected Graphs ◽  
Star Graphs ◽  
Graph Theoretic

AbstractWe study geometric presentations of braid groups for particles that are constrained to move on a graph, i.e. a network consisting of nodes and edges. Our proposed set of generators consists of exchanges of pairs of particles on junctions of the graph and of certain circular moves where one particle travels around a simple cycle of the graph. We point out that so defined generators often do not satisfy the braiding relation known from 2D physics. We accomplish a full description of relations between the generators for star graphs where we derive certain quasi-braiding relations. We also describe how graph braid groups depend on the (graph-theoretic) connectivity of the graph. This is done in terms of quotients of graph braid groups where one-particle moves are put to identity. In particular, we show that for 3-connected planar graphs such a quotient reconstructs the well-known planar braid group. For 2-connected graphs this approach leads to generalisations of the Yang–Baxter equation. Our results are of particular relevance for the study of non-abelian anyons on networks showing new possibilities for non-abelian quantum statistics on graphs.

Short and Simple Cycle Separators in Planar Graphs

2016 ◽  
Vol 21 ◽  
pp. 1-24 ◽  
Author(s):  
Eli Fox-Epstein ◽  
Shay Mozes ◽  
Phitchaya Mangpo Phothilimthana ◽  
Christian Sommer
Keyword(s):  
Planar Graphs ◽  
Simple Cycle

scholarly journals Erdös-Gyárfás Conjecture for Cubic Planar Graphs

10.37236/3252 ◽  
2013 ◽  
Vol 20 (2) ◽  
Author(s):  
Christopher Carl Heckman ◽  
Roi Krakovski
Keyword(s):  
Planar Graphs ◽  
Minimum Degree ◽  
Negative Integer ◽  
Simple Cycle ◽  
Discharging Method ◽  
Computer Based

In 1995, Paul Erdös and András Gyárfás conjectured that for every graph of minimum degree at least 3, there exists a non-negative integer $m$ such that $G$ contains a simple cycle of length $2^m$. In this paper, we prove that the conjecture holds for 3-connected cubic planar graphs. The proof is long, computer-based in parts, and employs the Discharging Method in a novel way.

Acute Constraints in Straight-Line Drawings of Planar Graphs

2019 ◽  
Vol E102.A (9) ◽  
pp. 994-1001
Author(s):  
Akane SETO ◽  
Aleksandar SHURBEVSKI ◽  
Hiroshi NAGAMOCHI ◽  
Peter EADES
Keyword(s):  
Planar Graphs ◽  
Line Drawings ◽  
Straight Line

A Space-Efficient Separator Algorithm for Planar Graphs

2019 ◽  
Vol E102.A (9) ◽  
pp. 1007-1016 ◽  
Author(s):  
Ryo ASHIDA ◽  
Sebastian KUHNERT ◽  
Osamu WATANABE
Keyword(s):  
Planar Graphs

Note on (semi-)proper orientation of some triangulated planar graphs

2021 ◽  
Vol 392 ◽  
pp. 125723
Author(s):  
Ruijuan Gu ◽  
Hui Lei ◽  
Yulai Ma ◽  
Zhenyu Taoqiu
Keyword(s):  
Planar Graphs ◽  
Proper Orientation
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