Long Paths in Bipartite Graphs and Path-Bistar Bipartite Ramsey Numbers

Abstract

In this paper, we focus on a so-called Fan-type condition assuring us the existence of long paths in bipartite graphs. As a consequence of our main result, we completely determine the bipartite Ramsey numbers $$b(P_{s},B_{t_{1},t_{2}})$$, where $$B_{t_{1},t_{2}}$$ is the graph obtained from a $$t_{1}$$-star and a $$t_{2}$$-star by joining their centers.