On partitions of hereditary properties of graphs

• Autorzy: Mieczysław Borowiecki , Anna Fiedorowicz
• 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

EN

hereditary property; acyclic colouring; Ramsey class

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 05C75: Structural characterization of families of graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2006
• Tom: 26
• Numer: 3
• Strony: 377-387

Daty

wydano

2006

otrzymano

2006-01-11

poprawiono

2006-09-21

Twórcy

autor

Mieczysław Borowiecki

• Faculty of Mathematics, Computer Science, and Econometrics, University of Zielona Góra, Prof. Z. Szafrana 4a, 65-516 Zielona Góra, Poland

autor

Anna Fiedorowicz

• 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.

Identyfikatory

DOI

10.7151/dmgt.1330