  In this work we improve on the bounds presented by Li&Li for network coding
gain in the undirected case. A tightened bound for the undirected multicast
problem with three terminals is derived. An interesting result shows that with
fractional routing, routing throughput can achieve at least 75% of the coding
throughput. A tighter bound for the general multicast problem with any number
of terminals shows that coding gain is strictly less than 2. Our derived bound
depends on the number of terminals in the multicast network and approaches 2
for arbitrarily large number of terminals.
