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On Pattern Ramsey Numbers of Graphs

On Pattern Ramsey Numbers of Graphs,10.1007/s00373-004-0562-y,Graphs and Combinatorics,Robert E. Jamison,Douglas B. West

On Pattern Ramsey Numbers of Graphs   (Citations: 12)
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A color pattern is a graph whose edges are partitioned into color classes. A family F of color patterns is a Ramsey family if there is some integer N such that every edge- coloring of KN has a copy of some pattern in F. The smallest such N is the (pattern) Ramsey number R(F ) of F. The classical Canonical Ramsey Theorem of Erd} os and Rado (4) yields an easy characterization of the Ramsey families of color patterns. In this paper we determine R(F ) for all families consisting of equipartitioned stars, and we prove that 5bs 1
Journal: Graphs and Combinatorics , vol. 20, no. 3, pp. 333-339, 2004
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    • ...As shown by Jamison and West [14], an (H;G)-good coloring of an arbitrarily large complete graph exists unless either G is a star or H is a forest...

    MARIA AXENOVICHet al. ON COLORINGS AVOIDING A RAINBOW CYCLE AND A FIXED MONOCHROMATIC SUBGRA...

    • ...Concerning the more general problem of considering general patterns of colors, Jamison and West [74] considered a particular family of colorings (equipartitioned stars) while Axenovich and Jamison [15] studied another family (F = {K lex n , K rain , H mono }). Notice this is related to the rainbow triangle free work dis-...

    Shinya Fujitaet al. Rainbow Generalizations of Ramsey Theory: A Survey

    • ... a combination of the two problems, Axenovich and Iverson [1] defined the mixed Ramsey numbers maxR(n, G, H) and minR(n, G, H) as the maximum (respectively, minimum) number of colours in an edge-colouring of Kn such that no monochromatic subgraph of Kn is isomorphic to G and no rainbow subgraph is isomorphic to H. They noted that the numbers are well-defined whenever the edges of G do not induce a star and H is not a forest (see also [9])...

    Veselin Jungicet al. A note on edge-colourings avoiding rainbow K_4 and monochromatic K_m

    • ...The constrained Ramsey number has been studied by many researchers [1, 3, 4, 7, 8, 10, 13, 14, 18], and the bipartite case in [2]...

    Po-shen Lohet al. Constrained Ramsey Numbers

    • ...On the other hand, the problem of nding unavoidable rainbow H or monochromatic G in any coloring of Kn for n large enough, has been studied in [18], when H is a forest and G is a star...
    • ...This is an easy observation which can also be found in [18]...

    Maria Axenovichet al. Edge-colorings avoiding rainbow and monochromatic subgraphs

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