For given two graphs G and H, the Ramsey number R(G, H) is the smallest positive integer n such that for every graph F of order n the following holds: either F contains G or the complement of F contains H. Let Fl be a linear forest, namely a disjoint union of paths with l vertices altogether, and Wm=K1 + Cm is a wheel with m + 1 vertices. Surahmat and Baskoro (2002) found that
R(Fl,Wm)={ 2l−1 for m even, m≥4 and for l≥m2(m−2);3l−2 for m odd, m≥5 and for l≥m2(m−2)
.
In this paper, we have rearrangement of the Ramsey number for a linear forest Fl versus wheel Wm that:
R(Fl,Wm)={ 2l−1 for m even, m≥4 and for l≥4;3l−2 for m odd, m≥5 and for l≥5
.
Topics
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