BOOK EMBEDDING OF TOROIDAL BIPARTITE GRAPHS

被引：4

作者：

Nakamoto, Atsuhiro ^{[1
]}

Ota, Katsuhiro ^{[2
]}

Ozeki, Kenta ^{[3
]}

机构：

[1] Yokohama Natl Univ, Dept Math, Hodogaya Ku, Yokohama, Kanagawa 2408501, Japan

[2] Keio Univ, Dept Math, Kohoku Ku, Yokohama, Kanagawa 223, Japan

[3] Res Org Informat & Syst, Natl Inst Informat, Chiyoda Ku, Tokyo 1018430, Japan

来源：

SIAM JOURNAL ON DISCRETE MATHEMATICS | 2012年 / 26卷 / 02期

关键词：

torus; even embedding; book embedding; quadrangulation; GENUS-G GRAPHS; PLANAR GRAPHS; PAGENUMBER; THICKNESS;

D O I：

10.1137/100794651

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Endo proved that every toroidal graph has a book embedding with at most seven pages. In this paper, we prove that every toroidal bipartite graph has a book embedding with at most five pages. In order to do so, we prove that every bipartite torus quadrangulation Q with n vertices admits two disjoint noncontractible simple closed curves cutting the torus into two annuli so that each of the two annuli contains a spanning connected subgraph of Q with exactly n edges satisfying a certain condition.

引用

页码：661 / 669

页数：9

共 50 条

[21] Book embedding of locally planar graphs on orientable surfaces
Nakamoto, Atsuhiro
Nozawa, Takayuki
DISCRETE MATHEMATICS, 2016, 339 (11) : 2672 - 2679
[22] On Topological Book Embedding for k-plane Graphs
Kaufmann, Michael
Kuckuk, Axel
GRAPH DRAWING AND NETWORK VISUALIZATION, 2019, 11904 : 596 - 598
[23] Bipartite graphs as polynomials and polynomials as bipartite graphs
Grinblat, Andrey
Lopatkin, Viktor
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2021, 20 (05)
[24] Convex bipartite graphs and bipartite circle graphs
Kizu, T
Haruta, Y
Araki, T
Kashiwabara, T
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 1998, E81A (05) : 789 - 795
[25] Packing bipartite graphs with covers of complete bipartite graphs
Chalopin, Jeremie
Paulusma, Daniel
DISCRETE APPLIED MATHEMATICS, 2014, 168 : 40 - 50
[26] GraPacking Bipartite Graphs with Covers of Complete Bipartite Graphs
Chalopin, Jeremie
Paulusma, Daniel
ALGORITHMS AND COMPLEXITY, PROCEEDINGS, 2010, 6078 : 276 - +
[27] BIPARTITE GRAPHS
JAGERS, AA
AMERICAN MATHEMATICAL MONTHLY, 1977, 84 (09): : 748 - 748
[28] MATRIX GRAPHS AND BIPARTITE GRAPHS
CHEN, WK
IEEE TRANSACTIONS ON CIRCUIT THEORY, 1965, CT12 (02): : 268 - &
[29] Bipartite graphs that are not circle graphs
Bouchet, A
ANNALES DE L INSTITUT FOURIER, 1999, 49 (03) : 809 - +
[30] On line graphs of bipartite graphs
Staton, W
UTILITAS MATHEMATICA, 1998, 53 : 183 - 187

← 1 2 3 4 5 →