On almost-planar graphs

被引：0
|
作者：
Ding, Guoli [1 ]
Fallon, Joshua [1 ]
Marshall, Emily [2 ]
机构：
[1] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA
[2] Arcadia Univ, Comp Sci & Math Dept, Glenside, PA USA
来源：
ELECTRONIC JOURNAL OF COMBINATORICS | 2018年 / 25卷 / 01期
关键词：
MATROIDS;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A nonplanar graph G is called almost-planar if for every edge e of G, at least one of G\e and G/e is planar. In 1990, Gubser characterized 3-connected almost-planar graphs in his dissertation. However, his proof is so long that only a small portion of it was published. The main purpose of this paper is to provide a short proof of this result. We also discuss the structure of almost-planar graphs that are not 3-connected.
引用
收藏
页数：14
相关论文
共 50 条
  • [1] Delta-wye reduction of almost-planar graphs
    Wagner, Donald K.
    DISCRETE APPLIED MATHEMATICS, 2015, 180 : 158 - 167
  • [2] An algorithm for delta-wye reduction of almost-planar graphs
    Gitler, Isidoro
    Sandoval-Angeles, Gustavo
    DISCRETE APPLIED MATHEMATICS, 2020, 285 : 631 - 641
  • [3] New infinite families of almost-planar crossing-critical graphs
    Hlineny, Petr
    ELECTRONIC JOURNAL OF COMBINATORICS, 2008, 15 (01):
  • [4] GLIMM SCHEME FOR SYSTEMS WITH ALMOST-PLANAR INTERACTIONS
    SCHOCHET, S
    COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1991, 16 (8-9) : 1423 - 1440
  • [5] ALMOST PANCYCLIC PLANAR GRAPHS
    MALKEVITCH, J
    NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 22 (04): : A452 - A452
  • [6] On the Crossing Number of Almost Planar Graphs
    Mohar, Bojan
    INFORMATICA-JOURNAL OF COMPUTING AND INFORMATICS, 2006, 30 (03): : 301 - 303
  • [7] On the crossing number of almost planar graphs
    Hlineny, Petr
    Salazar, Gelasio
    GRAPH DRAWING, 2007, 4372 : 162 - +
  • [8] Almost-Linear ε-Emulators for Planar Graphs
    Chang, Hsien-Chih
    Krauthgamer, Robert
    Tan, Zihan
    PROCEEDINGS OF THE 54TH ANNUAL ACM SIGACT SYMPOSIUM ON THEORY OF COMPUTING (STOC '22), 2022, : 1311 - 1324
  • [9] Almost Optimal Distance Oracles for Planar Graphs
    Charalampopoulos, Panagiotis
    Gawrychowski, Pawel
    Mozes, Shay
    Weimann, Oren
    PROCEEDINGS OF THE 51ST ANNUAL ACM SIGACT SYMPOSIUM ON THEORY OF COMPUTING (STOC '19), 2019, : 138 - 151
  • [10] THERE ARE PLANAR GRAPHS ALMOST AS GOOD AS THE COMPLETE GRAPH
    CHEW, LP
    JOURNAL OF COMPUTER AND SYSTEM SCIENCES, 1989, 39 (02) : 205 - 219
12345