A Note on Edge-Colourings Avoiding Rainbow $K_4$ and Monochromatic $K_m$
نویسندگان
چکیده
منابع مشابه
A Note on Edge-Colourings Avoiding Rainbow K4 and Monochromatic Km
We study the mixed Ramsey number maxR(n,Km,Kr), defined as the maximum number of colours in an edge-colouring of the complete graph Kn, such that Kn 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 maxR(n,Km,K4) ≤ n3/2 √ 2m for all m ≥ 3. Further, we discuss a possible way to impr...
متن کاملFe b 20 09 A note on edge - colourings avoiding rainbow K 4 and monochromatic
We study the mixed Ramsey number maxR(n,Km,Kr), defined as the maximum number of colours in an edge-colouring of the complete graph Kn, such that Kn 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 maxR(n,Km,K4) ≤ n3/2 √ 2m for all m ≥ 3. Further, we discuss a possible way to impr...
متن کاملEdge-colorings avoiding rainbow and monochromatic subgraphs
For two graphs G and H , let the mixed anti-Ramsey numbers, maxR(n; G, H), (minR(n; G, H)) be the maximum (minimum) number of colors used in an edge-coloring of a complete graph with n vertices having no monochromatic subgraph isomorphic to G and no totally multicolored (rainbow) subgraph isomorphic to H . These two numbers generalize the classical anti-Ramsey and Ramsey numbers, respectively. ...
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Let k and ` be positive integers. With a graph G, we associate the quantity ck,`(G), the number of k-colorings of the edge set of G with no monochromatic matching of size `. Consider the function ck,` : N −→ N given by ck,`(n) = max {ck,`(G) : |V (G)| = n}, the maximum of ck,`(G) over all graphs G on n vertices. In this paper, we determine ck,`(n) and the corresponding extremal graphs for all l...
متن کاملMonochromatic Cycle Partitions in Local Edge Colourings
An edge colouring of a graph is said to be an r-local colouring if the edges incident to any vertex are coloured with at most r colours. Generalising a result of Bessy and Thomassé, we prove that the vertex set of any 2-locally coloured complete graph may be partitioned into two disjoint monochromatic cycles of different colours. Moreover, for any natural number r, we show that the vertex set o...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2009
ISSN: 1077-8926
DOI: 10.37236/257