Keep going with this process until no such vertex \(v_l\) exists. Then continue in this manner (stop solving \(Q_2\) and start solving \(Q_3\)). Let \(v_l \ne v_k\) be the vertex with largest index such that \(v_k\) lies in another path (if such a vertex exists). A soon as the subgraph \(P_2 \,\square\, \lbrace v_k \rbrace \) contains exactly one peg and one hole, stop solving \(Q_1\) and start solving \(Q_2\). Let \(v_k \in Q_1\) be the vertex with largest index such that \(v_k\) lies in another path. Begin to solve \(P_2 \,\square\, Q_1\) using Theorem 1 or Lemma 1. Use this to decompose T into paths \(Q_1,\ldots ,Q_m\). Choose a root vertex \(v_0\) and do a depth-first-search, enumerating the vertices in the order they occur. If T is a path this follows from Theorem 1. It suffices to show that \(P_2 \,\square\, T\) is solvable. \(P_2 \,\square\, G\) is freely solvable for any connected graph G. The first step in doing this is to show that Cartesian products are solvable if one of the components is the path \(P_2\). Using the super free solvability of ladders, we can prove a fairly general result about Cartesian products. In that case G has solitaire number \(\mathrm \cdot v\), we can finally solve \(G_1\) with terminal peg in t.Äue to symmetry, this covers all cases. Strictly k- solvable, if G is k-solvable but not l-solvable for any \(lRegistrar of Record identified in this output may have an RDDS service that can be queried for additional information on how to contact the Registrant, Admin, or Tech contact of the queried domain name.In general, we begin with a starting state \(S \subset V\) of vertices that are empty (i.e., without pegs). By submitting this query, you agree to abide by this policy. Public Interest Registry reserves the right to modify these terms at any time. You agree that you will use this data only for lawful purposes and that, under no circumstances will you use this data to (a) allow, enable, or otherwise support the transmission by e-mail, telephone, or facsimile of mass unsolicited, commercial advertising or solicitations to entities other than the data recipient's own existing customers or (b) enable high volume, automated, electronic processes that send queries or data to the systems of Registry Operator, a Registrar, or Donuts except as reasonably necessary to register domain names or modify existing registrations. This service is intended only for query-based access. The data in this record is provided by Public Interest Registry for informational purposes only, and Public Interest Registry does not guarantee its accuracy. Terms of Use: Access to Public Interest Registry WHOIS information is provided to assist persons in determining the contents of a domain name registration record in the Public Interest Registry registry database. URL of the ICANN Whois Inaccuracy Complaint Form: įor more information on Whois status codes, please visit Tech Email: Please query the RDDS service of the Registrar of Record identified in this output for information on how to contact the Registrant, Admin, or Tech contact of the queried domain name. Tech State/Province: REDACTED FOR PRIVACY Registrant Email: Please query the RDDS service of the Registrar of Record identified in this output for information on how to contact the Registrant, Admin, or Tech contact of the queried domain name.Īdmin State/Province: REDACTED FOR PRIVACYĪdmin Email: Please query the RDDS service of the Registrar of Record identified in this output for information on how to contact the Registrant, Admin, or Tech contact of the queried domain name. Registrant Phone Ext: REDACTED FOR PRIVACY Registrant Postal Code: REDACTED FOR PRIVACY Registrant Organization: archimedes laboratory Registry Registrant ID: REDACTED FOR PRIVACY Registrar Abuse Contact Phone: 1.8777228662
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