Ramsey Numbers Involving Graphs with Long Suspended Paths
Ramsey Numbers Involving Graphs with Long Suspended Paths
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DOI：
10.1112/jlms/s2-24.3.405
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发表时间：
1981-12
影响因子：
1.2
通讯作者：
S. Burr
中科院分区：
文献类型：
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作者：
S. Burr
求一个色数为χ的图，且图中任意颜色为χ的任意点着色的任意颜色类中的最小点数。任意连通图，任意与h同胚的点图。证明了如果足够大，拉姆齐数（G,Hn）满足r(G,Hn) = (χ−1)(n−1)+t。还表明，对于某物g，当它是一个带点的星时，没有这样的结果成立。
LetGbe a graph with chromatic number χ and withtbeing the minimum number of points in any color class of any point-coloring ofGwith χ colors. LetHbe any connected graph and letHnbe a graph onnpoints which is homeomorphic toH. It is proved that ifnis large enough, the Ramsey numberr(G,Hn) satisfiesr(G,Hn) = (χ − l)(n−l) +t. It is also shown that for someG, no such result holds whenHnis a star withnpoints.