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\@writefile{toc}{\contentsline {author}{Ciaran McCreesh\unskip {} \and Patrick Prosser \and James Trimble}{1}}
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\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces A Stable Roomates (SR) instance on the left sr6, with 6 agents. In the middle an instance of Stable Marriage (SM) with three men and three women, sm3. On the right, sm3 is represented as an instance of Stable Roommates with Incomplete lists (SRI), instance sri6. Instance sr6 has two stable matchings, namely $\{(1,5),(2,3),(4,6)\}$ and $\{(1,4),(2,3),(5,6)\}$. Instance sm3 has a single stable matching $\{(1,1),(2,2),(3,3)\}$. Instance sri6 has only one stable matching $\{(1,4),(2,5),(3,6)\}$ and this corresponds to the stable matching for sm3.}}{2}}
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\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Increasing the proportion $p$ of agents found to be acceptable in stable roommates. On the x axis $p$, probability that two agents find each other acceptable. On the left, the y axis is percentage of instances that admit a stable matching. On the right, y axis is average size of stable matching when one exists. Note that when an instance admits a stable matching, all its stable matchings are the same size \cite  {gi89}. Contours are shown for even ($n=100$) and odd ($n=101$) number of agents.}}{6}}
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