On Ramsey Minimal Graphs
نویسندگان
چکیده
A graph G is r-ramsey-minimal with respect to Kk if every rcolouring of the edges of G yields a monochromatic copy of Kk, but the same is not true for any proper subgraph of G. In this paper we show that for any integer k ≥ 3 and r ≥ 2, there exists a constant c > 1 such that for large enough n, there exist at least c 2 non-isomorphic graphs on at most n vertices, each of which is r-ramsey-minimal with respect to the complete graph Kk. Furthermore, in the case r = 2, we give an asymmetric version of the above result.
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ورودعنوان ژورنال:
- SIAM J. Discrete Math.
دوره 22 شماره
صفحات -
تاریخ انتشار 2008