The minor crossing number

SIAM Journal on Discrete Mathematics

Volumn 20, Issue 2, 2006, Pages 344-356

  Bokal, Drago ^a   Fijavž, Gašper ^b   Mohar, Bojan ^b,c  

^a INSTITUTE OF MATHEMATICS   (Slovenia)

^b UNIVERSITY OF LJUBLJANA   (Slovenia)

^c SIMON FRASER UNIVERSITY   (Canada)

Author keywords

Crossing number; Graph minor

Indexed keywords

BOUNDARY CONDITIONS; PROBLEM SOLVING;

CROSSING NUMBER; GRAPH MINOR;

GRAPH THEORY;

EID: 33847292626     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/05062706X     Document Type: Article

References (20)

1. D. ARCHDEACON, Problems in Topological Graph Theory, Department of Mathematics and Statistics, University of Vermont, Burlington, VT; online at http://www.emba.uvm.edu/ ~archdeac/problems/minorcr.htm, 1995.
2. D. ARCHDEACON, A Kuratowski theorem for the protective plane, J. Graph Theory, 5 (1981), pp. 243-246.
3. S. N. BHATT AND F. T. LEIGHTON, A framework for solving VLSI graph layout problems, J. Comput. System Sci., 28 (1984), pp. 300-343.
4. G. FIJAVŽ, Graph Minors and Connectivity, Ph.D. thesis, Department of Mathematics, University of Ljubljana, Slovenia, 2001 (in Slovene).
5. n is as conjectured for n ≥ m(m+ 1), J. Graph Theory, 47 (2004), pp. 53-72.
6. P. HLINĚNÝ, Crossing number is hard for cubic graphs (extended abstract), in Math Foundations of Computer Science MFCS 2004, Lecture Notes in Comput. Sci. 3153, Springer-Verlag, New York, 2004, pp. 772-782.
7. H. H. GLOVER, J. P. HUNEKE, AND C.-S. WANG, 103 graphs that are irreducible for the projective plane, J. Combin. Theory Ser. B, 27 (1979), pp. 332-370.
8. M. JUVAN AND B. MOHAR, An Algorithm for Embedding Graphs in the Torus, manuscript.
9. K. KURATOWSKI, Sur le problème des courbes gauches en topologie, Fund. Math., 15 (1930), pp. 271-283.
10. F. T. LEIGHTON, Complexity Issues in VLSI, MIT Press, Cambridge, MA, 1983.
11. F. T. LEIGHTON, New lower bound techniques for VLSI, Math. Systems Theory, 17 (1984), pp. 47-70.
12. T. MADEJ, Bounds for the crossing number of the N-cube, J. Graph Theory, 15 (1991), pp. 81-97.
13. D. MCQUILLAN AND R. B. RICHTER, On 3-regular graphs having crossing number at least 2, J. Graph Theory, 18 (1994), pp. 831-893.
14. B. MOHAR, Protective planarity in linear time, J. Algorithms, 15 (1993), pp. 482-502.
15. B. MOHAR AND C. THOMASSEN, Graphs on Surfaces, Johns Hopkins University Press, Baltimore, MD, 2001.
16. E. G. MORENO AND G. SALAZAR, Bounding the crossing number of a graph in terms of the crossing number of a minor with small maximum degree, J. Graph Theory, 36 (2001), pp. 168-173.
17. R. B. RICHTER, Cubic graphs with crossing number two, J. Graph Theory, 12 (1988), pp. 363-374.
18. N. ROBERTSON AND P. SEYMOUR, Excluding a graph with one crossing, Contemp. Math., 147 (1993), pp. 669-675.
19. O. SÝKORA AND I. VRŤO, On crossing numbers of hypercubes and cube connected cycles, BIT, 33 (1993), pp. 232-237.
20. I. VRŤO, Crossing number of graphs: A bibliography, Institute of Mathematics, Slovak Academy of Sciences, Bratislava, Slovak Republic; available online from ftp://ftp.ifi.savba.sk/pub/ imrich/crobib.pdf.