Ramsey Number for Some Brooms

Abstract:

For a given graph G, Ramsey number R(G) is the smallest integer N such that any red/blue edgecoloring of KN contains a red copy or a blue copy of G. Let broom Bk,m be a tree obtained by identifying the central vertex of a star K1,k with an endvertex of Pm. It is proven that R(Bk,2k-1)=4k-2 and R(Bk,4)=2k+3 for integer k>1.