of France had married Otto's sister Gerberga in 939, and Otto's son Liudolf had married Ida, the daughter of Hermann I, Duke of Swabia, in 947. The former dynastically tied the royal house of West Francia to that of East Francia, and the latter secured his son's succession to the Duchy of Swabia, as Hermann had no sons. Otto's plans came to fruition when, in 950, Liudolf became Duke of Swabia, and in 954 Otto's nephew Lothair of France became King of France. In 944, Otto appointed Conrad the Red as Duke of Lorraine and brought him into his extended family through his marriage to Otto's daughter Liutgarde in 947. A Salian Frank by birth, Conrad was a nephew of former king Conrad I of Germany. Following the death of Otto's uncle Berthold, Duke of Bavaria, in 947, Otto satisfied his brother Henry's ambition through his marriage to Judith, Duchess of Bavaria, daughter of Arnulf, Duke of Bavaria, and appointed him as the new Duke of Bavaria in 948. This arrangement finally achieved peace between the brothers, as Henry thereafter abandoned his claims to the throne. Through his familial ties to the dukes, Otto had strengthened the sovereignty of the crown and the overall cohesiveness of the kingdom. On 29 January 946, Eadgyth died suddenly at the age of 35, and Otto buried his wife in the Cathedral of Magdeburg. The union had lasted sixteen years and produced two children; with Eadgyth's death, Otto began to make arrangements for his succession. Like his father before him, Otto intended to transfer sole rule of the kingdom to his son Liudolf upon his death. Otto called together all leading figures of the kingdom and had them swear an oath of allegiance to Liudolf, thereby promising to recognize his sole claim to the throne as Otto's heir apparent. Relying on recent archaeological evidences, Bachrach estimates that the armies he mobilized in 953 and 954 should have been in the range of 20,000 to 25,000 men, which were needed to besiege cities such as Mainz, which was defended by armies in excess of 30,000. Foreign relations France The West Frankish kings had lost considerable royal power after internal struggles with their aristocracy, but still asserted their authority over the Duchy of Lorraine, a territory also claimed by East Francia. The German king was supported by Louis IV's chief domestic rival, Hugh the Great. Louis