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1999 | 19 | 2 | 159-166
Tytuł artykułu

Remarks on the existence of uniquely partitionable planar graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider the problem of the existence of uniquely partitionable planar graphs. We survey some recent results and we prove the nonexistence of uniquely (𝓓₁,𝓓₁)-partitionable planar graphs with respect to the property 𝓓₁ "to be a forest".
Wydawca
Rocznik
Tom
19
Numer
2
Strony
159-166
Opis fizyczny
Daty
wydano
1999
otrzymano
1999-02-02
poprawiono
1999-09-21
Twórcy
  • Institute of Mathematics, Technical University Zielona Góra, Poland
autor
  • Faculty of Economics, Technical University Košice, Slovakia
autor
  • Computer and Automation Institute, Hungarian Academy of Sciences Budapest, Hungary
autor
  • Institute of Mathematics, Technical University Ilmenau, Germany
Bibliografia
  • [1] C. Bazgan, M. Santha and Zs. Tuza, On the approximation of finding a(nother) Hamiltonian cycle in cubic Hamiltonian graphs, in: Proc. STACS'98, Lecture Notes in Computer Science 1373 (Springer-Verlag, 1998) 276-286. Extended version in the J. Algorithms 31 (1999) 249-268.
  • [2] C. Berge, Theorie des Graphes, Paris, 1958.
  • [3] C. Berge, Graphs and Hypergraphs, North-Holland, 1973.
  • [4] B. Bollobás and A.G. Thomason, Uniquely partitionable graphs, J. London Math. Soc. 16 (1977) 403-410, doi: 10.1112/jlms/s2-16.3.403.
  • [5] M. Borowiecki, I. Broere, M. Frick, P. Mihók and G. Semanišin, Survey of hereditary properties of graphs, Discuss. Math. Graph Theory 17 (1997) 5-50, doi: 10.7151/dmgt.1037.
  • [6] I. Broere and J. Bucko, Divisibility in additive hereditary graph properties and uniquely partitionable graphs, Tatra Mountains 18 (1999) 79-87.
  • [7] J. Bucko, M. Frick, P. Mihók and R. Vasky, Uniquely partitionable graphs, Discuss. Math. Graph Theory 17 (1997) 103-114, doi: 10.7151/dmgt.1043.
  • [8] J. Bucko and J. Ivanco, Uniquely partitionable planar graphs with respect to properties having a forbidden tree, Discuss. Math. Graph Theory 19 (1999) 71-78, doi: 10.7151/dmgt.1086.
  • [9] J. Bucko, P. Mihók and M. Voigt Uniquely partitionable planar graphs, Discrete Math. 191 (1998) 149-158, doi: 10.1016/S0012-365X(98)00102-2.
  • [10] G. Chartrand and J.P. Geller, Uniquely colourable planar graphs, J. Combin. Theory 6 (1969) 271-278, doi: 10.1016/S0021-9800(69)80087-6.
  • [11] F. Harary, S.T. Hedetniemi and R.W. Robinson, Uniquely colourable graphs, J. Combin. Theory 6 (1969) 264-270; MR39#99.
  • [12] P. Mihók, Reducible properties and uniquely partitionable graphs, in: Contemporary Trends in Discrete Mathematics, From DIMACS and Dimatia to the Future, Proceedings of the DIMATIA-DIMACS Conference, Stirin May 1997, Ed. R.L. Graham, J. Kratochvil, J. Ne setril, F.S. Roberts, DIMACS Series in Discrete Mathematics, Volume 49, AMS, 213-218.
  • [13] P. Mihók, G. Semanišin and R. Vasky, Hereditary additive properties are uniquely factorizable into irreducible factors, J. Graph Theory 33 (2000)44-53, doi: 10.1002/(SICI)1097-0118(200001)33:1<44::AID-JGT5>3.0.CO;2-O
  • [14] J. Mitchem, Uniquely k-arborable graphs, Israel J. Math. 10 (1971) 17-25; MR46#81.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1092
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