The Planar Slope Number of Subcubic Graphs

被引：0

作者：

Di Giacomo, Emilio ^{[1
]}

Liotta, Giuseppe ^{[1
]}

Montecchiani, Fabrizio ^{[1
]}

机构：

[1] Univ Perugia, Dip Ingn, I-06100 Perugia, Italy

来源：

LATIN 2014: THEORETICAL INFORMATICS | 2014年 / 8392卷

关键词：

CUBIC GRAPHS;

D O I：

暂无

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

A subcubic planar graph is a planar graph whose vertices have degree at most three. We show that the subcubic planar graphs with at least five vertices have planar slope number at most four, which is worst case optimal. This answers an open question by Jelinek et al. [6]. As a corollary, we prove that the subcubic planar graphs with at least five vertices have angular resolution pi/4, which solves an open problem by Kant [7] and by Formann et al. [4].

引用

页码：132 / 143

页数：12

共 50 条

[1] Star list chromatic number of planar subcubic graphs
Min Chen
André Raspaud
Weifan Wang
[J]. Journal of Combinatorial Optimization, 2014, 27 : 440 - 450
[2] Star list chromatic number of planar subcubic graphs
Chen, Min
Raspaud, Andre
Wang, Weifan
[J]. JOURNAL OF COMBINATORIAL OPTIMIZATION, 2014, 27 (03) : 440 - 450
[3] Induced Matchings in Subcubic Planar Graphs
Kang, Ross J.
Mnich, Matthias
Mueller, Tobias
[J]. ALGORITHMS-ESA 2010, PT II, 2010, 6347 : 112 - +
[4] INDUCED MATCHINGS IN SUBCUBIC PLANAR GRAPHS
Kang, Ross J.
Mnich, Matthias
Muller, Tobias
[J]. SIAM JOURNAL ON DISCRETE MATHEMATICS, 2012, 26 (03) : 1383 - 1411
[5] Exact square coloring of subcubic planar graphs
Foucaud, Florent
Hocquard, Herve
Mishra, Suchismita
Narayanan, Narayanan
Naserasr, Reza
Sopena, Eric
Valicov, Petru
[J]. DISCRETE APPLIED MATHEMATICS, 2021, 293 : 74 - 89
[6] On Lower Bounds for the Matching Number of Subcubic Graphs
Haxell, P. E.
Scott, A. D.
[J]. JOURNAL OF GRAPH THEORY, 2017, 85 (02) : 336 - 348
[7] On the packing chromatic number of subcubic outerplanar graphs
Gastineau, Nicolas
Holub, Premysl
Togni, Olivier
[J]. DISCRETE APPLIED MATHEMATICS, 2019, 255 : 209 - 221
[8] Choosability of the square of planar subcubic graphs with large girth
Havet, F.
[J]. DISCRETE MATHEMATICS, 2009, 309 (11) : 3553 - 3563
[9] Subcubic planar graphs of girth 7 are class I
Bonduelle, Sebastien
Kardos, Frantisek
[J]. DISCRETE MATHEMATICS, 2022, 345 (10)
[10] Injective choosability of subcubic planar graphs with girth 6
Brimkov, Boris
Edmond, Jennifer
Lazar, Robert
Lidicky, Bernard
Messerschmidt, Kacy
Walker, Shanise
[J]. DISCRETE MATHEMATICS, 2017, 340 (10) : 2538 - 2549

← 1 2 3 4 5 →