Mr Reitwiesner shows four ways in which the rulers of Lesbos are ancestors of the above-mentioned individuals. What caught my eye and made me think was the part about the "Legitimist" claimant to the Monegasque throne. Then something occured to me.
It is widely known that John William Friso, Prince of Orange (1687 - 1711) and his wife, Landgravine Marie Louise of Hesse-Kassel (1688 - 1765), are the most recent common ancestors of all current European hereditary monarchs, as well as of many pretenders to abolished thrones on the continent. The descents are all through legitimate and recognised marriages.
Thing is, there is one monarch for whom this does not quite apply and that is Prince Albert II of Monaco. His paternal grandmother, Princess Charlotte, Duchess of Valentinois (1898 - 1977), was born unambiguously illegitimate and it was through the intervention of the French Republic that she was legitimated and put in the line of succession.
In that case, who is the "true" most recent common ancestor of present-day European royalty? Genealogics was going to be of enormous help here.
If Prince Rainier's mother was disqualified, then I had to examine the ancestry of his father, Prince Pierre, Duke of Valentinois (1895 - 1964). Unfortunately, he was not a close relative of his wife. I had noticed that both were descended from Lorenzo Mancini, (1602 –1650), a brother-in-law of Cardinal Mazarin (1602 - 1661). According to Genealogics, Pierre was the seventh cousin of his wife's paternal great-grandfather, Charles III - see here
That wasn't much help, sadly. I thought of giving up and asking Peter for help.
Long story short, it is neither William the Conqueror (as may be tempting to think) nor Geoffrey Plantagenet, Count of Anjou (1113 - 1151), as Genealogics had suggested (sort of).
The MRCA was actually Peter.
To be slightly more specific, the relevant couple is Peter I, Duke of Bourbon (1311 - 1356) and Isabella of Valois, Duchess of Bourbon (1313 - 1383).
As our Peter has pointed out many times in his genealogical threads, Holy Roman Emperor Ferdinand I is a universal ancestor of European royalty today. This link
shows his descent from the Duke of Bourbon.
Now, let us see how Pierre of Bourbon leads to Pierre of Polignac:
Pierre I, Duc de Bourbon > Marguerite de Bourbon > Marguerite d'Albret > Isabelle de Foix > Seigneur Guy de Pons, Vicomte de Turenne > Antoinette de Pons, Dame de Montfort > François II de La Tour, Vicomte de Turenne, Baron de Montgascon > Claude de La Tour > Just Louis IV de Tournon, Comte de Roussillon, Baron de Durteil > Françoise de Tournon > Louis Armand XIX de Polignac, Vicomte de Polignac > Scipion de Polignac, Vicomte de Polignac, Marquis de Chalencon > Louis Héracle Armand XXI, Vicomte de Polignac > Jules François Armand, 1.Duc de Polignac > Melchior, Comte de Polignac > Charles, Comte de Polignac > Maxence, Comte de Polignac > Pierre, Comte de Polignac, Duc de Valentinois
So, how did I do?