problems connecting to mysql server across network... arg!!

[Mike]

Hi all.

Right now I have two linux boxes running fedora core 4 on my home network, with mysqld up and running on "hostname_1" (a desktop). I want to log into the mysql server on the desktop using a mysql client on my laptop ("hostname_2"). Simple enough... but I must be missing something. check it out:

[user@hostname_1]$ mysqladmin ping -h hostname_1
mysqld is alive

[user@hostname_2]$ mysqladmin ping -h hostname_1
mysqladmin: connect to server at 'hostname_1' failed
error: 'Lost connection to MySQL server during query'

but then if I netstat it....
[user@hostname_1]$ netstat -ltp
Active Internet connections (only servers)
Proto Recv-Q Send-Q Local Address Foreign Address State PID/Program name
....... ------- ......
tcp 0 0 *:mysql *:* LISTEN -
....... ------- ......

and nmap gives me:
[root@hostname_1]$ nmap -sT -O hostname_1
PORT STATE SERVICE
..... ------ .......
3306/tcp open mysql
..... ------- .......

So it looks like the mysql server is up and running and listening on hostname_1.... but I can't figure out why I can't connect to it with the mysql client on hostname_2. Any ideas??

thanks a bunch, take it easy

Mike (linux & mysql semi-newbie)