On an anti‐Ramsey threshold for sparse graphs with one triangle
On an anti‐Ramsey threshold for sparse graphs with one triangle
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关于具有一个三角形的稀疏图的反拉姆齐阈值
作者：
Y. Kohayakawa;P. B. Konstadinidis;G. Mota
For graphs G and H, let G→p rb H denote the property that for every proper edge‐coloring of G (with an arbitrary number of colors) there is a rainbow copy of H in G, that is, a copy of H with no two edges of the same color. The authors (2014) proved that, for every graph H, the threshold function pH rb =pH rb (n) of this property for the binomial random graph G(n,p) is asymptotically at most n−1/m(2)(H) , where m(2)(H) denotes the so‐called maximum 2‐density of H. Nenadov et al. (2014) proved that if H is a cycle with at least seven vertices or a complete graph with at least 19 vertices, then pH rb =n−1/m(2)(H) . We show that there exists a fairly rich, infinite family of graphs F containing a triangle such that if p≥Dn−β for suitable constants D=D(F)>0 and β=β(F) , where β>1/m(2)(F) , then G(n,p)→p rb F almost surely. In particular, pF rb ≪n−1/m(2)(F) for any such graph F.
关于随机图中的 KÅR 猜想
影响因子：
1
作者：
D. Conlon;W. T. Gowers;W. Samotij;M. Schacht
通讯作者：
M. Schacht