Completing Partial Packings of Bipartite Graphs [article]

Zoltán Füredi, Ago-Erik Riet, Mykhaylo Tyomkyn
2010 arXiv   pre-print
Given a bipartite graph H and an integer n, let f(n;H) be the smallest integer such that, any set of edge disjoint copies of H on n vertices, can be extended to an H-design on at most n+f(n;H) vertices. We establish tight bounds for the growth of f(n;H) as n →∞. In particular, we prove the conjecture of Füredi and Lehel FuLe that f(n;H) = o(n). This settles a long-standing open problem.
arXiv:1007.4287v3 fatcat:yyz257hapbc33gfdi4jppnmd2y