메뉴 건너뛰기




Volumn 76, Issue 1-2, 2006, Pages 165-176

On the crossing number of complete graphs

Author keywords

Complete graph; Crossing number; Enumeration; Order types

Indexed keywords

COMPLETE GRAPHS; CROSSING NUMBER; ENUMERATION; ORDER TYPES;

EID: 27644564296     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00607-005-0133-3     Document Type: Article
Times cited : (18)

References (29)
  • 2
    • 0141465284 scopus 로고    scopus 로고
    • Enumerating order types for small point sets with applications
    • Aichholzer, O., Aurenhammer, F., Krasser, H.: Enumerating order types for small point sets with applications. Order 19, 265-281 (2002).
    • (2002) Order , vol.19 , pp. 265-281
    • Aichholzer, O.1    Aurenhammer, F.2    Krasser, H.3
  • 7
    • 51249175187 scopus 로고
    • Some provably hard crossing number problems
    • Bienstock, D.: Some provably hard crossing number problems. Discrete Comput. Geometry 6, 443-459 (1991).
    • (1991) Discrete Comput. Geometry , vol.6 , pp. 443-459
    • Bienstock, D.1
  • 10
    • 0002436460 scopus 로고
    • Crossing number problems
    • Erdös, P., Guy, R. K.: Crossing number problems. Am. Math. Month. 88, 52-58 (1973).
    • (1973) Am. Math. Month. , vol.88 , pp. 52-58
    • Erdös, P.1    Guy, R.K.2
  • 12
  • 14
    • 0010247787 scopus 로고
    • On the number of crossings in a complete graph
    • Harary, F., Hill, A.: On the number of crossings in a complete graph. Proc. Edinburgh Math. Soc. 13(2), 333-338 (1962).
    • (1962) Proc. Edinburgh Math. Soc. , vol.13 , Issue.2 , pp. 333-338
    • Harary, F.1    Hill, A.2
  • 15
    • 0000391389 scopus 로고
    • A lower bound for the optimal crossing-free Hamiltonian cycle problem
    • Hayward, R. B.: A lower bound for the optimal crossing-free Hamiltonian cycle problem. Discrete Comput. Geometry 2, 327-343 (1987).
    • (1987) Discrete Comput. Geometry , vol.2 , pp. 327-343
    • Hayward, R.B.1
  • 16
    • 0348023369 scopus 로고
    • An upper bound for the rectilinear crossing number of the complete graph
    • Jensen, H. F.: An upper bound for the rectilinear crossing number of the complete graph. J. Combinatorial Theory B 29, 212-216 (1971).
    • (1971) J. Combinatorial Theory B , vol.29 , pp. 212-216
    • Jensen, H.F.1
  • 18
    • 24144478640 scopus 로고    scopus 로고
    • Convex quadrilaterals and k-sets
    • Towards a theory of geometric graphs (Pach J., ed.)
    • Lovász, L., Vesztergombi, K., Welzl, E., Wagner, U.: Convex quadrilaterals and k-sets. In: Towards a theory of geometric graphs (Pach J., ed.). AMS Contemporary Mathematics Ser. 342, 139-148 (2004).
    • (2004) AMS Contemporary Mathematics Ser. , vol.342 , pp. 139-148
    • Lovász, L.1    Vesztergombi, K.2    Welzl, E.3    Wagner, U.4
  • 19
    • 0034311833 scopus 로고    scopus 로고
    • Which crossing number is it, anyway?
    • Pach, J., Tóth, G.: Which crossing number is it, anyway? J. Combinatorial Theor. B 80, 225-246 (2000).
    • (2000) J. Combinatorial Theor. B , vol.80 , pp. 225-246
    • Pach, J.1    Tóth, G.2
  • 20
    • 0010249478 scopus 로고    scopus 로고
    • Thirteen problems on crossing numbers
    • Pach, J., Tóth, G.: Thirteen problems on crossing numbers. Geombinatorics 9, 195-207 (2000).
    • (2000) Geombinatorics , vol.9 , pp. 195-207
    • Pach, J.1    Tóth, G.2
  • 21
    • 0031504393 scopus 로고    scopus 로고
    • Relations between crossing numbers of complete and complete bipartite graphs
    • Richter, R.B., Thomassen, C.: Relations between crossing numbers of complete and complete bipartite graphs. Am. Math. Month. 104, 131-137 (1997).
    • (1997) Am. Math. Month. , vol.104 , pp. 131-137
    • Richter, R.B.1    Thomassen, C.2
  • 22
    • 21844519141 scopus 로고
    • The rectilinear crossing number of a complete graph and Sylvester's "four point problem" of geometric probability
    • Scheinerman, E.R., Wilf, H.S.: The rectilinear crossing number of a complete graph and Sylvester's "four point problem" of geometric probability. Am. Math. Month. 101, 939-943 (1994).
    • (1994) Am. Math. Month. , vol.101 , pp. 939-943
    • Scheinerman, E.R.1    Wilf, H.S.2
  • 24
    • 0030478525 scopus 로고    scopus 로고
    • A parallel stochastic optimization algorithm for finding mappings of the rectilinear minimal crossing number
    • Thorpe, J. T., Harris, F. C.: A parallel stochastic optimization algorithm for finding mappings of the rectilinear minimal crossing number. Ars Combinatorica 43, 135-148 (1996).
    • (1996) Ars Combinatorica , vol.43 , pp. 135-148
    • Thorpe, J.T.1    Harris, F.C.2
  • 25
    • 0002156092 scopus 로고
    • Toward a theory of crossing numbers
    • Tutte, W. T.: Toward a theory of crossing numbers. J. Combinatorial Theor. 8, 45-53 (1970).
    • (1970) J. Combinatorial Theor. , vol.8 , pp. 45-53
    • Tutte, W.T.1
  • 27
    • 0010251536 scopus 로고    scopus 로고
    • On crossing numbers, and some unsolved problems
    • Cambridge: Cambridge University Press
    • Wilf, H. S.: On crossing numbers, and some unsolved problems. In: Combinatorics, geometry, and probability. Cambridge: Cambridge University Press 1997, pp. 557-562.
    • (1997) Combinatorics, Geometry, and Probability , pp. 557-562
    • Wilf, H.S.1
  • 28
    • 84861271414 scopus 로고    scopus 로고
    • http://www.ist.tugraz.at/aichholzer/crossings.html
  • 29
    • 84861268382 scopus 로고    scopus 로고
    • http://www.igi.tugraz.at/hkrasser/data/d36.nb


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.