Planar Ramsey numbers

• Autorzy: Izolda Gorgol
• Języki publikacji: EN

Abstrakty

EN

The planar Ramsey number PR(G,H) is defined as the smallest integer n for which any 2-colouring of edges of Kₙ with red and blue, where red edges induce a planar graph, leads to either a red copy of G, or a blue H. In this note we study the weak induced version of the planar Ramsey number in the case when the second graph is complete.

Słowa kluczowe

EN

Ramsey number; planar graph; induced subgraph

Kategorie tematyczne

• 05D10: Ramsey theory
• 05C55: Generalized Ramsey theory

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2005
• Tom: 25
• Numer: 1-2
• Strony: 45-50

Daty

wydano

2005

otrzymano

2003-10-24

poprawiono

2005-01-13

Twórcy

autor

Izolda Gorgol

• Department of Applied Mathematics, Lublin University of Technology, Nadbystrzycka 38, 20-618 Lublin, Poland

Bibliografia

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• [12] V. Rödl, A generalization of Ramsey theorem (Ph.D. thesis, Charles University, Prague, Czech Republic, 1973) 211-220.
• [13] R. Steinberg and C.A. Tovey, Planar Ramsey number, J. Combin. Theory (B) 59 (1993) 288-296, doi: 10.1006/jctb.1993.1070.
• [14] K. Walker, The analog of Ramsey numbers for planar graphs, Bull. London Math. Soc. 1 (1969) 187-190, doi: 10.1112/blms/1.2.187.

Identyfikatory

DOI

10.7151/dmgt.1258