Local Properties via Color Energy Graphs and Forbidden Configurations
Local Properties via Color Energy Graphs and Forbidden Configurations
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DOI：
10.1137/18m1225987
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发表时间：
2018-10
期刊：
影响因子：
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通讯作者：
Sara Fish;C. Pohoata;Adam Sheffer
中科院分区：
文献类型：
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作者：
Sara Fish;C. Pohoata;Adam Sheffer
ErdHo、S和Shelah的局部性质问题推广了许多Ramsey问题和一些明显的距离问题。在这项工作中，我们得到了局部性质问题及其变种的各种新的界。我们通过继续发展颜色能量技术来做到这一点-加性组合数学中加性能量概念的变体。特别地，我们将颜色能量的概念推广到更高的颜色能量，并将其与极值图论中关于没有圈或没有大小为$k$的细分的图的结果相结合。
The local properties problem of Erd\H{o}s and Shelah generalizes many Ramsey problems and some distinct distances problems. In this work, we derive a variety of new bounds for the local properties problem and its variants. We do this by continuing to develop the color energy technique --- a variant of the concept of additive energy from Additive Combinatorics. In particular, we generalize the concept of color energy to higher color energies, and combine these with Extremal Graph Theory results about graphs with no cycles or subdivisions of size $k$.