All root CAs are self-signed. Which means we feel forced to implicitly trust that the CA is operated responsibly and securely. This isn't always the case (Diginotar).
There are alternatives to the certificate authority method. One of these is the web of trust, which is used mainly in PGP / GPG / OpenPGP implementations.
There are situations that can arise in PKI implementations where we need one PKI to "trust" another. This is called cross-signing or cross certification.
One of the key components of a PKI is an LDAP directory service. This is where signed certificates and revocation information are published to be publicly available. The directory takes the form of a tree structure. Each entry in the tree forms part of the entry's distinguished name (DName). An example being CN=NRC, OU=IT, O=MyOrg, C=GB. In this DName the root element is C, which is a country, followed by O, for organisation, OU, org unit and CN, which is common name. Each DName element is an entry in the directory tree, which has a specific schema object class. The object class defines the mandatory and optional attributes for an entry. The CN element is usually represented in LDAP terms by the schema object class called inetorgperson, however specialized types have been developed for PKI purposes. The full LDAP schema for PKI objects is defined here.
Included in this is the definition of the PKI CA Object Class. This includes the crossCertificatePair Attribute. Using this attribute extra certificates for the CA can be issued by another CA (as in your diagram). This means, although the core CA certificate is self-signed, for cross-certification purposes its trust anchor is another root CA. Indeed, if RootCA1 signs a cross certification certificate for RootCA2, then RootCA2 may also sign a cross certification certificate for RootCA1. Indeed, as you have specified in your question, it is possible through cross certification to have the ring situation, where RootCA1 signs RootCA2, RootCA2 signs RootCA3 and RootCA3 signs RootCA1. Validation of cross certified CAs requires that the validation process look up cross certified certificates in the LDAP entry for the CA, because there is no reference to these in the Root CA certificate (the self-signed "core" certificate), although there should be a reference to the LDAP entry for the CA in the Subject Information Access extension.
When taking into account cross certification, certificate path validation can become an incredibly complex process. However, specialized software services have been developed which allow users to "outsource" the complex process to trusted validation authorities. These services are called online certificate status protocol and server-based certificate validation protocol servers. The Axway VA is a server which includes both OCSP and SCVP in one and can be configured to provide full certificate path validation in cross certified CA environments.