Yum: No package mysql-server available in Cent OS 7

In RHEL 7, and consequently in CentOS7, the mysql- packages (or most of them, anyway) have been replaced with mariadb- packages due to an upstream rename/fork. Simply yum install mariadb-server mariadb-libs mariadb and you should be okay - the command names themselves are still mostly mysql related.

As answered by John mysql is replaced with mariadb in RHEL 7 and later, but you can still install mysql. Follow the following steps:

1. Download and add the repository, then update.

   wget http://repo.mysql.com/mysql-community-release-el7-5.noarch.rpm
   sudo rpm -ivh mysql-community-release-el7-5.noarch.rpm
   yum update
   

2. Install MySQL as usual and start the service. During installation, you will be asked if you want to accept the results from the .rpm file’s GPG verification. If no error or mismatch occurs, enter y.

   sudo yum install mysql-server
   sudo systemctl start mysqld
   

Ref: linode

On any RPM based OS you can find which package provides MySQL server:

yum provides "*bin/mysqld"