Arguably the most important relationship presented in the book is between Eliezer and his father, Chlomo. It is a dynamic and ever changing relationship.
At the beginning of the story, it is clear that Eliezer respects his father, and acknowledges his place of importance in their small town, but in his awe and reverence, does not have a very close personal relationship with him. He seeks spiritual counsel and wisdom and when his father initially scoffs at Elie's young age, he goes to Moshe the Beadle.
Everything changes, however, once Eliezer and his father remain together in the concentration camps. It becomes the goal of each, to remain alive, and to remain together. The bond between father and son is seen as much stronger through Chlomo's worry and protection of his son, a fact which Eliezer frequently notes and laments returning in the same fashion. In section 5, Chlomo is certain he will be chosen in the next selection and gifts to his son an "inheritance" of his spoon and knife. When his father survives this selection, Eliezer's attitude seems to shift as he realizes the importance of his father's life to his own survival.
Later, in section 7, after the remaining prisoners have been run several miles through the snow, they are boarded on a train and several prisoners fall asleep into their deaths. At one point, Eliezer frantically shakes his father awake, in the fear that his body will be thrown from the train. In this moment Eliezer admits that if his father were to die, he has no reason to live.
As his father's health begins to decline from dysentary, however, Eliezer does find the will to survive with or without his father. His guilt is overridden by his survival instinct. He knows that his father is suffering, and death would end this suffering. He knows also that his father's death would free him from the burden of looking after him. When his father finally does die, Elie has no tears, but only a lingering feeling of relief.
The changing relationship between father and son is one that could only have been brought on by such dire circumstances as were presented in the Holocaust. It could be argued that Elie ultimately survives because of his father's presence, leadership, and will to sacrifice himself if it meant his son could live.