Math Problem Unsolved for 40 Years Finally Cracked
Researchers have resolved a foundational graph theory problem that has stumped mathematicians since the 1980s. The breakthrough could accelerate algorithm design for networks, logistics, and data optimization—areas where understanding graph structure directly impacts computational efficiency and real-world system performance.
Originaltitel: Long Induced Paths in Ks,s‐Free Graphs
ABSTRACT More than 40 years ago, Galvin, Rival, and Sands showed that every ‐free graph containing an ‐vertex path must contain an induced path of length , where as . Recently, it was shown by Duron, Esperet, and Raymond that one can take . In this note, we give a short self‐contained proof that a ‐free graph with an ‐vertex path contains an induced path of length at least . Combined with the recent remarkable example of Couëtoux, Defrain, and Raymond, which provides an upper bound of , this essentially resolves this old problem.