Let G be a connected graph on n vertices with no more than n(\ + e) edges, and Pkor Cka path or cycle with k vertices. In this paper we will show that if n is sufficiently large and e is sufficiently small then for k odd r(G> Ck) = In - 1. Also, for k > 2, r(G, pk) _ max(n + [k/2] — 1, n + k - 2 — α' - δ), where a' is the independence number of an appropriate subgraph of G and 6 is 0 or 1 depending upon /t, k and a.
ASJC Scopus subject areas
- Applied Mathematics