  We study the approximate core for edge cover games, which are cooperative
games stemming from edge cover problems. In these games, each player controls a
vertex on a network $G = (V, E; w)$, and the cost of a coalition $S\subseteq V$
is equivalent to the minimum weight of edge covers in the subgraph induced by
$S$. We prove that the 3/4-core of edge cover games is always non-empty and can
be computed in polynomial time by using linear program duality approach. This
ratio is the best possible, as it represents the integrality gap of the natural
LP for edge cover problems. Moreover, our analysis reveals that the ratio of
approximate core corresponds with the length of the shortest odd cycle of
underlying graphs.
