New lower bounds on the size-Ramsey number of a path (Q2073313)

Summary: We prove that for all graphs with at most \((3.75-o(1))n\) edges there exists a 2-coloring of the edges such that every monochromatic path has order less than \(n\). This was previously known to be true for graphs with at most \(2.5n-7.5\) edges. We also improve on the best-known lower bounds in the \(r\)-color case.