scholarly journals Long cycles in 4-connected planar graphs

2009 ◽  
Vol 309 (5) ◽  
pp. 1051-1059 ◽  
Author(s):  
Qing Cui ◽  
Yumei Hu ◽  
Jian Wang
Keyword(s):  
Planar Graphs ◽  
Long Cycles

scholarly journals Long cycles and spanning subgraphs of locally maximal 1‐planar graphs

2020 ◽  
Vol 95 (1) ◽  
pp. 125-137
Author(s):  
I. Fabrici ◽  
J. Harant ◽  
T. Madaras ◽  
S. Mohr ◽  
R. Soták ◽  
...  
Keyword(s):  
Planar Graphs ◽  
Spanning Subgraphs ◽  
Locally Maximal ◽  
Long Cycles

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

scholarly journals A Discussion of a Cryptographical Scheme Based in F-Critical Sets of a Latin Square

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 285
Author(s):  
Laura M. Johnson ◽  
Stephanie Perkins
Keyword(s):  
Necessary Conditions ◽  
Latin Square ◽  
Latin Squares ◽  
Critical Sets ◽  
Long Cycles ◽  
The Given

This communication provides a discussion of a scheme originally proposed by Falcón in a paper entitled “Latin squares associated to principal autotopisms of long cycles. Applications in cryptography”. Falcón outlines the protocol for a cryptographical scheme that uses the F-critical sets associated with a particular Latin square to generate access levels for participants of the scheme. Accompanying the scheme is an example, which applies the protocol to a particular Latin square of order six. Exploration of the example itself, revealed some interesting observations about both the structure of the Latin square itself and the autotopisms associated with the Latin square. These observations give rise to necessary conditions for the generation of the F-critical sets associated with certain autotopisms of the given Latin square. The communication culminates with a table which outlines the various access levels for the given Latin square in accordance with the scheme detailed by Falcón.

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

scholarly journals Distributed Dominating Set Approximations beyond Planar Graphs

2019 ◽  
Vol 15 (3) ◽  
pp. 1-18 ◽  
Author(s):  
Saeed Akhoondian Amiri ◽  
Stefan Schmid ◽  
Sebastian Siebertz
Keyword(s):  
Planar Graphs ◽  
Dominating Set

scholarly journals Clustered 3-colouring graphs of bounded degree

2021 ◽  
pp. 1-13
Author(s):  
Vida Dujmović ◽  
Louis Esperet ◽  
Pat Morin ◽  
Bartosz Walczak ◽  
David R. Wood
Keyword(s):  
Planar Graphs ◽  
Maximum Degree ◽  
Bounded Degree ◽  
Bounded Number ◽  
Proper Vertex ◽  
Vertex Colouring

Abstract A (not necessarily proper) vertex colouring of a graph has clustering c if every monochromatic component has at most c vertices. We prove that planar graphs with maximum degree $\Delta$ are 3-colourable with clustering $O(\Delta^2)$ . The previous best bound was $O(\Delta^{37})$ . This result for planar graphs generalises to graphs that can be drawn on a surface of bounded Euler genus with a bounded number of crossings per edge. We then prove that graphs with maximum degree $\Delta$ that exclude a fixed minor are 3-colourable with clustering $O(\Delta^5)$ . The best previous bound for this result was exponential in $\Delta$ .

Structure and pancyclicity of maximal planar graphs with diameter two

2021 ◽  
Author(s):  
Shu-Yu Cui ◽  
Yiqiao Wang ◽  
Danjun Huang ◽  
Hongwei Du ◽  
Weifan Wang
Keyword(s):  
Planar Graphs
Sign in / Sign up

Export Citation Format

Share Document