Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  828.05040
Autor:  Erdös, Paul; Gyárfás, András
Title:  Vertex covering with monochromatic paths. (In English)
Source:  Math. Pannonica 6, No.1, 7-10 (1995).
Review:  This note proves that if the edges of Kn are colored red and blue, then for each integer l > 0, there exist l monochromatic paths of a common color whose union covers n({l+1\over l+2}) vertices. This Ramseyian result is a sharp generalization of the result of L. Gerencsér and the second author [On Ramsey type problems, Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Math. 10, 167-170 (1967; Zbl 163.45502)] that there is a path of at least \lfloor {{2n} \over 3} \rfloor+1 vertices.
Reviewer:  G.L.McColm (Tampa)
Classif.:  * 05C55 Generalized Ramsey theory
                   05C38 Paths and cycles
                   05C15 Chromatic theory of graphs and maps
Keywords:  vertex covering; path covering; monochromatic paths
Citations:  Zbl 163.455

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