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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 682.05046

**Autor: ** Burr, Stefan A.; Erdös, Paul; Graham, Ronald L.; Sós, V.T.

**Title: ** Maximal anti-Ramsey graphs and the strong chromatic number. (In English)

**Source: ** J. Graph Theory 13, No.3, 263-282 (1989).

**Review: ** Let G and L denote two graphs. By \chi_{s}(G < L) we mean the minimum number of colors required to color the vertices of G so that any subgraph of G isomorphic to L has all of its vertices assigned different colors. Given integers n and e, \chi_{s}(n,e,L) = **max**_{G in G}**{**\chi_{s}(G,L)**}** where *G* is the class of all graphs on n vertices with e edges. Thus, \chi_{s}(n,e,L) is an ``extremal anti- Ramsey number''. This paper is devoted to the study of these numbers. It contains some specific values, some bounds and some asymptotic results. It closes with a discussion of several interesting open questions.

**Reviewer: ** J.E.Graver

**Classif.: ** * 05C55 Generalized Ramsey theory

05C15 Chromatic theory of graphs and maps

**Keywords: ** extremal anti-Ramsey number

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