Triangulated edge intersection graphs of paths in a tree
نویسندگان
چکیده
منابع مشابه
Triangulated edge intersection graphs of paths in a tree
Let T = (V(T), E(T)) be a tree and B = {Pi} denote a collection of non-trivial (i.e., of length at least 1) simple paths in T, where a path P= (v,, u2, . . . , Q) is considered in the sequel as the collection {{uJ, {Q}, . . . ,{z)J, {u,, u2}, {u2, I+}, _ . . , {w,-,, Q}}. The intersection graph 0(S, 9) of 9 over set S has vertices which correspond to the paths in 9 and two vertices uk and U! ar...
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Let P be a collection of nontrivial simple paths in a tree T . The edge intersection graph of P , denoted by EPT (P), has vertex set that corresponds to the members of P , and two vertices are joined by an edge if the corresponding members of P share a common edge in T . An undirected graph G is called an edge intersection graph of paths in a tree, if G = EPT (P) for some P and T . The EPT grap...
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The class of edge intersection graphs of a collection of paths in a tree (EPT graphs) is investigated, where two paths edge intersect if they share an edge. The cliques of an EPT graph are characterized and shown to have strong Helly number 4. From this it is demonstrated that the problem of finding a maximum clique of an EPT graph can be solved in polynomial time. It is shown that the strong p...
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In this paper we continue the investigation of the class of edge intersection graphs of a collection of paths in a tree (EPT graphs) where two paths edge intersect if they share an edge. The class of EPT graphs differs from the class known as path graphs, the latter being the class of vertex intersection graphs of paths in a tree. A characterization is presented here showing when a path graph i...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1985
ISSN: 0012-365X
DOI: 10.1016/0012-365x(85)90050-0