No offence, but you need to read up on the Domain Name Service.
Domain Name System - Wikipedia, the free encyclopedia
Any computer can run a DNS server, but it must be registered and bound to the DNS Back-bone servers using A records etc.
Any computer can run a Name-Server, but that also has to be linked with your DNS server in order to propogate Domain Names correctly.
In theory,
if the DNS Back-Bone supports ".travel" suffixes within it's NameServer for registering Domain Names, the amount of Domain Names available to each suffix is endless, just like with ".com", etc...
The only competition involved would be if two companies tried to buy something like "www.HelloWorld.travel"