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2003 | 23 | 2 | 333-363
Tytuł artykułu

On a special case of Hadwiger's conjecture

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Hadwiger's Conjecture seems difficult to attack, even in the very special case of graphs G of independence number α(G) = 2. We present some results in this special case.
Wydawca
Rocznik
Tom
23
Numer
2
Strony
333-363
Opis fizyczny
Daty
wydano
2003
otrzymano
2001-09-29
poprawiono
2002-05-13
Twórcy
  • Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240, USA
  • Institute of Mathematics, TU Ilmenau, D-98684 Ilmenau, Germany
autor
  • Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
Bibliografia
  • [1] C. Berge, Alternating chain methods: a survey, in: Graph Theory and Computing, ed., R. Read (Academic Press, New York, 1972) 1-13.
  • [2] S. Brandt, On the structure of dense triangle-free graphs, Combin. Prob. Comput. 8 (1999) 237-245, doi: 10.1017/S0963548399003831.
  • [3] S. Brandt and T. Pisanski, Another infinite sequence of dense triangle-free graphs, Elect. J. Combin. 5 (1998) #R43 1-5.
  • [4] P.A. Catlin, Hajós' graph-coloring conjecture: variations and counterexamples, J. Combin. Theory (B) 26 (1979) 268-274, doi: 10.1016/0095-8956(79)90062-5.
  • [5] G.A. Dirac, Some theorems on abstract graphs, Proc. London Math. Soc. 2 (1952) 69-81, doi: 10.1112/plms/s3-2.1.69.
  • [6] G.A. Dirac, Trennende Knotenpunktmengen und Reduzibilität abstrakter Graphen mit Anwendung auf das Vierfarbenproblem, J. Reine Angew. Math. 204 (1960) 116-131, doi: 10.1515/crll.1960.204.116.
  • [7] P. Duchet and H. Meyniel, On Hadwiger's number and the stability number, Ann. Discrete Math. 13 (1982), 71-74.
  • [8] T. Gallai, Kritische Graphen II, Publ. Math. Inst. Hung. Acad. 8 (1963) 373-395.
  • [9] M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness (W.H. Freeman and Company, San Francisco, 1979).
  • [10] H. Hadwiger, Über eine Klassifikation der Streckenkomplexe, Vierteljahrsschrift der Naturf. Gesellschaft in Zürich 88 (1943) 133-142.
  • [11] J.H. Kim, The Ramsey number R(3,t) has order of magnitude t²/log t, Random Struct. Algorithms 7 (1995) 173-207, doi: 10.1002/rsa.3240070302.
  • [12] U. Krusenstjerna-Hafstrø m and B. Toft, Some remarks on Hadwiger's Conjecture and its relation to a conjecture of Lovász, in: The Theory and Applications of Graphs: Proceedings of the Fourth International Graph Theory Conference, Kalamazoo, 1980, eds., G. Chartrand, Y. Alavi, D.L. Goldsmith, L. Leśniak-Foster and D.R. Lick (John Wiley and Sons, 1981) 449-459.
  • [13] L. Lovász and M.D. Plummer, Matching Theory, Akadémiai Kiadó, Budapest and Ann. Discrete Math. 29 (North-Holland, Amsterdam, 1986) 448.
  • [14] W. Mader, Über trennende Eckenmengen in homomorphiekritischen Graphen, Math. Ann. 175 (1968) 243-252, doi: 10.1007/BF02052726.
  • [15] J. Pach, Graphs whose every independent set has a common neighbor, Discrete Math. 37 (1981) 217-228, doi: 10.1016/0012-365X(81)90221-1.
  • [16] N. Robertson, P.D. Seymour and R. Thomas, Hadwiger's conjecture for K₆-free graphs, Combinatorica 13 (1993) 279-362, doi: 10.1007/BF01202354.
  • [17] B. Toft, On separating sets of edges in contraction-critical graphs, Math. Ann. 196 (1972) 129-147, doi: 10.1007/BF01419610.
  • [18] B. Toft, A survey of Hadwiger's Conjecture, Congr. Numer. 115 (1996) 249-283.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1206
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