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2006 | 26 | 3 | 377-387
Tytuł artykułu

On partitions of hereditary properties of graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper a concept 𝓠-Ramsey Class of graphs is introduced, where 𝓠 is a class of bipartite graphs. It is a generalization of well-known concept of Ramsey Class of graphs. Some 𝓠-Ramsey Classes of graphs are presented (Theorem 1 and 2). We proved that 𝓣₂, the class of all outerplanar graphs, is not 𝓓₁-Ramsey Class (Theorem 3). This results leads us to the concept of acyclic reducible bounds for a hereditary property 𝓟 . For 𝓣₂ we found two bounds (Theorem 4). An improvement, in some sense, of that in Theorem is given.
Słowa kluczowe
Wydawca
Rocznik
Tom
26
Numer
3
Strony
377-387
Opis fizyczny
Daty
wydano
2006
otrzymano
2006-01-11
poprawiono
2006-09-21
Twórcy
  • Faculty of Mathematics, Computer Science, and Econometrics, University of Zielona Góra, Prof. Z. Szafrana 4a, 65-516 Zielona Góra, Poland
  • Faculty of Mathematics, Computer Science, and Econometrics, University of Zielona Góra, Prof. Z. Szafrana 4a, 65-516 Zielona Góra, Poland
Bibliografia
  • [1] P. Boiron, E. Sopena and L. Vignal, Acyclic improper colorings of graphs, J. Graph Theory 32 (1999) 97-107, doi: 10.1002/(SICI)1097-0118(199909)32:1<97::AID-JGT9>3.0.CO;2-O
  • [2] P. Boiron, E. Sopena and L. Vignal, Acyclic improper colourings of graphs with bounded degree, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 49 (1999) 1-9.
  • [3] O.V. Borodin, On acyclic colorings of planar graphs, Discrete Math. 25 (1979) 211-236, doi: 10.1016/0012-365X(79)90077-3.
  • [4] O.V. Borodin, A.V. Kostochka, A. Raspaud and E. Sopena, Acyclic colourings of 1-planar graphs, Discrete Applied Math. 114 (2001) 29-41, doi: 10.1016/S0166-218X(00)00359-0.
  • [5] O.V. Borodin, A.V. Kostochka and D.R. Woodall, Acyclic colorings of planar graphs with large girth, J. London Math. Soc. 60 (1999) 344-352, doi: 10.1112/S0024610799007942.
  • [6] M. Borowiecki, I. Broere, M. Frick, P. Mihók and G. Semanišin, A survey of hereditary properties of graphs, Discussiones Mathematicae Graph Theory 17 (1997) 5-50, doi: 10.7151/dmgt.1037.
  • [7] M.I. Burstein, Every 4-valent graph has an acyclic 5-coloring, Soobsc. Akad. Gruzin. SSR 93 (1979) 21-24 (in Russian).
  • [8] G. Ding, B. Oporowski, D.P. Sanders and D. Vertigan, Partitioning graphs of bounded tree-width, Combinatorica 18 (1998) 1-12, doi: 10.1007/s004930050001.
  • [9] R. Diestel, Graph Theory (Springer, Berlin, 1997).
  • [10] B. Grunbaum, Acyclic coloring of planar graphs, Israel J. Math. 14 (1973) 390-412, doi: 10.1007/BF02764716.
  • [11] P. Mihók and G. Semanišin, Reducible properties of graphs, Discuss. Math. Graph Theory 15 (1995) 11-18, doi: 10.7151/dmgt.1002.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1330
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