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%Write your title here: 
\noindent{\bf\Large Path Graphs, Clique Trees, and Flowers\footnote{With apologies to Jack Edmonds.}}


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\noindent \underline{Lalla Mouatadid}, Robert Robere -- {\small University of Toronto}


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\noindent{\bf Abstract:} %Here write your abstract
A classical result by Lekkerkerker and Boland showed that interval graphs are precisely the chordal graphs that do not have asteroidal triples \cite{6}. Similar to Lekkerkerker and Boland, Cameron, Hoáng and Lévêque gave a characterization of directed path graphs by a “special type” of asteroidal triple, and asked whether or not there was such a characterization for path graphs \cite{4}. We give strong evidence that asteroidal triples alone are insufficient to characterize the family of path graphs, and give a new characterization of path graphs via a forbidden induced subgraph family that we call sun systems. Key to our new characterization is the study of asteroidal sets in sun systems, which are a natural generalization of asteroidal triples. 

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\bibitem{4}
	Cameron, K., Ho{\`{a}}ng, C.T., L{\'{e}}v{\^{e}}que, B.: 
	Characterizing directed path graphs by forbidden asteroids.
	Journal of Graph Theory 68(2), 103-112 (2011)
	
\bibitem{6}
	Lekkerkerker, C.G, Boland, J.C.:
	Representation of a finite graph by a set of intervals on the real line.
	Fundamenta Mathematicae 51, 45-64 (1962)	
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