ON THE CROSSING NUMBERS OF CARTESIAN PRODUCTS OF WHEELS AND TREES

被引：26

作者：

Klesc, Marian ^{[1
]}

Petrillova, Jana ^{[1
]}

Valo, Matus ^{[1
]}

机构：

[1] Tech Univ, Dept Math & Theoret Informat, Fac Elect Engn & Informat, Kosice 04200, Slovakia

来源：

DISCUSSIONES MATHEMATICAE GRAPH THEORY | 2017年 / 37卷 / 02期

关键词：

graph; drawing; crossing number; join product; Cartesian product; PATHS;

D O I：

10.7151/dmgt.1957

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Bokal developed an innovative method for finding the crossing numbers of Cartesian product of two arbitrarily large graphs. In this article, the crossing number of the join product of stars and cycles are given. Afterwards, using Bokal's zip product operation, the crossing numbers of the Cartesian products of the wheel Wn and all trees T with maximum degree at most five are established. © 2017, University of Zielona Gora. All rights reserved.

引用

页码：399 / 413

页数：15

共 24 条

[1]

[Anonymous], 1973, Nanta. Math.

[2] On the crossing numbers of Cartesian products with trees [J].

Bokal, Drago .

JOURNAL OF GRAPH THEORY, 2007, 56 (04) :287-300

[3] On the crossing numbers of Cartesian products with paths [J].

Bokal, Drago .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 2007, 97 (03) :381-384

[4] A branch-and-cut approach to the crossing number problem [J].

Buchheim, Christoph ;

Chimani, Markus ;

Ebner, Dietmar ;

Gutwenger, Carsten ;

Juenger, Michael ;

Klau, Gunnar W. ;

Mutzel, Petra ;

Weiskircher, Rene .

DISCRETE OPTIMIZATION, 2008, 5 (02) :373-388

[5]

Chimani M., 2016, LEIBNIZ INT P INFORM, V57, DOI [10.4230/LIPIcs.ESA.2016.29, DOI 10.4230/LIPICS.ESA.2016.29]

[6]

Chimani M., 2009, ACM J EXP ALGORITHMI, V14

[7]

Chimani M, 2008, LECT NOTES COMPUT SC, V5193, P284, DOI 10.1007/978-3-540-87744-8_24

[8] The crossing number of Cm x Cn is as conjectured for n≥m(m+1) [J].

Glebsky, LY ;

Salazar, G .

JOURNAL OF GRAPH THEORY, 2004, 47 (01) :53-72

[9]

Hanfei Mei, 2007, International Journal of Mathematical Combinatorics, V1, P33

[10] The crossing number of K1,4,n [J].

Huang, Yuanqiu ;

Zhao, Tinglei .

DISCRETE MATHEMATICS, 2008, 308 (09) :1634-1638

← 1 2 3 →