A note on edge-colourings avoiding rainbow K-4 and monochromatic K-m

JUNGIC, V; TS KAISER and Daniel KRÁĽ. A note on edge-colourings avoiding rainbow K-4 and monochromatic K-m. Electronic Journal of Combinatorics. Newark, USA: ELECTRONIC JOURNAL OF COMBINATORICS, 2009, vol. 16, No 1, 9 pp. ISSN 1077-8926.

Basic information

Original name

A note on edge-colourings avoiding rainbow K-4 and monochromatic K-m

Authors

JUNGIC, V; TS KAISER and Daniel KRÁĽ

Edition

Electronic Journal of Combinatorics, Newark, USA, ELECTRONIC JOURNAL OF COMBINATORICS, 2009, 1077-8926

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Other information

Language

English

Type of outcome

Article in a journal

Confidentiality degree

is not subject to a state or trade secret

Impact factor

Impact factor: 0.605

UT WoS

000266915900001

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Abstract

In the original language

We study the mixed Ramsey number max R(n, K-m, K-r),defined as the maximum number of colours in an edge-colouring of the complete graph K-n, such that K-n has no monochromatic complete subgraph on m vertices and no rainbow complete subgraph on r vertices. Improving an upper bound of Axenovich and Iverson, we show that max R(n, K-m, K-4) <= n(3/2) root 2m for all m >= 3. Further, we discuss a possible way to improve their lower bound on max R(n, K-4, K-4) based on incidence graphs of finite projective planes.