Tight competitive ratios of classic matching algorithms in the fully online model

Huang et al. (STOC 2018) introduced the fully online matching problem, a generalization of the classic online bipartite matching problem in that it allows all vertices to arrive online and considers general graphs. They showed that the ranking algorithm by Karp et al. (STOC 1990) is strictly better than 0.5-competitive and the problem is strictly harder than the online bipartite matching problem in that no algorithms can be (1 --- 1/e)-competitive.