Let r≥3 be an integer such that r−2 is a prime power and let H be a connected graph on n vertices with average degree at least d andα(H)≤βn,where 0<β<1 is a constant.We prove that the size Ramsey number R^(...Let r≥3 be an integer such that r−2 is a prime power and let H be a connected graph on n vertices with average degree at least d andα(H)≤βn,where 0<β<1 is a constant.We prove that the size Ramsey number R^(H;r)>nd2(r−2)2−Cn−−√for all sufficiently large n,where C is a constant depending only on r,d andβ.In particular,for integers k≥1,and r≥3 such that r−2 is a prime power,we have that there exists a constant C depending only on r and k such that R^(Pkn;r)>kn(r−2)2−Cn−−√−(k2+k)2(r−2)2 for all sufficiently large n,where P k n is the kth power of Pn.展开更多
基金This paper is supported by the National Natural Science Foundation of China(No.1217010182).
文摘Let r≥3 be an integer such that r−2 is a prime power and let H be a connected graph on n vertices with average degree at least d andα(H)≤βn,where 0<β<1 is a constant.We prove that the size Ramsey number R^(H;r)>nd2(r−2)2−Cn−−√for all sufficiently large n,where C is a constant depending only on r,d andβ.In particular,for integers k≥1,and r≥3 such that r−2 is a prime power,we have that there exists a constant C depending only on r and k such that R^(Pkn;r)>kn(r−2)2−Cn−−√−(k2+k)2(r−2)2 for all sufficiently large n,where P k n is the kth power of Pn.
